Atkin-Lehner |
2- 7+ 19- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
61712i |
Isogeny class |
Conductor |
61712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
752640 |
Modular degree for the optimal curve |
Δ |
-1642996047523437824 = -1 · 28 · 74 · 194 · 295 |
Discriminant |
Eigenvalues |
2- -1 -1 7+ -3 5 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-295316,-87187268] |
[a1,a2,a3,a4,a6] |
Generators |
[14189:1688834:1] |
Generators of the group modulo torsion |
j |
-11126181736405205584/6417953310638429 |
j-invariant |
L |
4.332412376439 |
L(r)(E,1)/r! |
Ω |
0.0997469359979 |
Real period |
R |
5.4292549606782 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995536 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15428b1 |
Quadratic twists by: -4 |