Atkin-Lehner |
2+ 7- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
112112w |
Isogeny class |
Conductor |
112112 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
135168 |
Modular degree for the optimal curve |
Δ |
-869063523328 = -1 · 210 · 73 · 114 · 132 |
Discriminant |
Eigenvalues |
2+ -2 -2 7- 11- 13- 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1864,53892] |
[a1,a2,a3,a4,a6] |
Generators |
[-32:286:1] [23:154:1] |
Generators of the group modulo torsion |
j |
-2040329596/2474329 |
j-invariant |
L |
7.6882428472844 |
L(r)(E,1)/r! |
Ω |
0.80394476863946 |
Real period |
R |
0.59769675314822 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000603 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
56056s1 112112o1 |
Quadratic twists by: -4 -7 |