Atkin-Lehner |
2- 3- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312dc |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
78 |
Product of Tamagawa factors cp |
deg |
2276352 |
Modular degree for the optimal curve |
Δ |
-1.1090856008997E+20 |
Discriminant |
Eigenvalues |
2- 3- -2 -1 0 5 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2313769,1445540855] |
[a1,a2,a3,a4,a6] |
Generators |
[842:9747:1] |
Generators of the group modulo torsion |
j |
-19692240832/1594323 |
j-invariant |
L |
6.3030093014975 |
L(r)(E,1)/r! |
Ω |
0.18381780228455 |
Real period |
R |
0.43960819111419 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000094 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312ch1 34656v1 69312cs1 |
Quadratic twists by: -4 8 -19 |