Enter a curve: The curve is [0,0,1,-7,6] A test of invariants: The curve is [0,0,1,-7,6] b2 = 0 b4 = -14 b6 = 25 b8 = -49 c4 = 336 c6 = -5400 disc = 5077 (# real components = 2) #torsion not yet computed The minimal curve is [0,0,1,-7,6] (reduced minimal model) b2 = 0 b4 = -14 b6 = 25 b8 = -49 c4 = 336 c6 = -5400 disc = 5077 (# real components = 2) #torsion not yet computed A test of Tate's algorithm: [0,0,1,-7,6] (reduced minimal model) b2 = 0 b4 = -14 b6 = 25 b8 = -49 c4 = 336 c6 = -5400 disc = 5077 (bad primes: [ 5077 ]; # real components = 2) #torsion not yet computed Conductor = 5077 Full display: [0,0,1,-7,6] (reduced minimal model) b2 = 0 b4 = -14 b6 = 25 b8 = -49 c4 = 336 c6 = -5400 disc = 5077 (bad primes: [ 5077 ]; # real components = 2) #torsion not yet computed Conductor = 5077 Global Root Number = -1 Reduction type at bad primes: p ord(d) ord(N) ord(j) Kodaira c_p root_number 5077 1 1 1 I1 1 1 Traces of Frobenius: p=2: ap=-2 p=3: ap=-3 p=5: ap=-4 p=7: ap=-4 p=11: ap=-6 p=13: ap=-4 p=17: ap=-4 p=19: ap=-7 p=23: ap=-6 p=29: ap=-6 p=31: ap=-2 p=37: ap=0 p=41: ap=0 p=43: ap=-8 p=47: ap=-9 p=53: ap=-9 p=59: ap=-11 p=61: ap=-2 p=67: ap=-12 p=71: ap=-8 p=73: ap=-14 p=79: ap=9 p=83: ap=-2 p=89: ap=11 p=97: ap=6 Testing construction from a non-integral model: After scaling down by 60, coeffs are [0,0,1/216000,-7/12960000,1/7776000000] Constructed curve is [0,0,1,-7,6] with scale = 60 Testing quadratic twists Base curve: [0,-1,1,0,0] conductor 11 Twist by -1 is [0,1,0,-5,-13] conductor 176 Twist by 2 is [0,1,0,-1,1] conductor 704 Twist by -2 is [0,-1,0,-1,-1] conductor 704 Twist by 3 is [0,0,0,-48,304] conductor 1584 Twist by -3 is [0,0,1,-3,-5] conductor 99 Prime twists: p = 2: Twist is [0,1,0,-5,-13] conductor 176 Twist is [0,-1,0,-1,-1] conductor 704 Twist is [0,1,0,-1,1] conductor 704 p = 3: Twist is [0,0,1,-3,-5] conductor 99 p = 5: Twist is [0,1,1,-8,19] conductor 275 p = 7: Twist is [0,1,1,-16,-66] conductor 539 p = 11: Twist is [0,-1,1,-40,-221] conductor 121 p = 13: Twist is [0,-1,1,-56,405] conductor 1859 p = 17: Twist is [0,1,1,-96,832] conductor 3179 p = 19: Twist is [0,1,1,-120,-1247] conductor 3971 p = 23: Twist is [0,-1,1,-176,-2082] conductor 5819 p = 29: Twist is [0,1,1,-280,4197] conductor 9251 All 16 quadratic twists supported on {2,3,5}: [0,-1,1,0,0] conductor 11 [0,1,0,-5,-13] conductor 176 [0,-1,0,-1,-1] conductor 704 [0,1,0,-1,1] conductor 704 [0,0,1,-3,-5] conductor 99 [0,0,0,-48,304] conductor 1584 [0,0,0,-12,38] conductor 6336 [0,0,0,-12,-38] conductor 6336 [0,1,1,-8,19] conductor 275 [0,-1,0,-133,-1363] conductor 4400 [0,1,0,-33,-187] conductor 17600 [0,-1,0,-33,187] conductor 17600 [0,0,1,-75,-594] conductor 2475 [0,0,0,-1200,38000] conductor 39600 [0,0,0,-300,4750] conductor 158400 [0,0,0,-300,-4750] conductor 158400