Atkin-Lehner |
3+ 7- 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
69531f |
Isogeny class |
Conductor |
69531 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
307200 |
Modular degree for the optimal curve |
Δ |
-200648742061383 = -1 · 32 · 77 · 114 · 432 |
Discriminant |
Eigenvalues |
-1 3+ 0 7- 11- -6 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-84918,9513594] |
[a1,a2,a3,a4,a6] |
Generators |
[136:641:1] |
Generators of the group modulo torsion |
j |
-575618923356625/1705486167 |
j-invariant |
L |
2.5785522835947 |
L(r)(E,1)/r! |
Ω |
0.56659661864291 |
Real period |
R |
0.56886861808469 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997046 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9933b1 |
Quadratic twists by: -7 |