Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312bp |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
-135497855048193216 = -1 · 26 · 38 · 199 |
Discriminant |
Eigenvalues |
2+ 3- 1 -1 5 4 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-135495,-26163729] |
[a1,a2,a3,a4,a6] |
Generators |
[60030:555579:125] |
Generators of the group modulo torsion |
j |
-91368216064/45001899 |
j-invariant |
L |
9.4634024282936 |
L(r)(E,1)/r! |
Ω |
0.12157204929816 |
Real period |
R |
2.4325601780372 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999694 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312n1 34656w1 3648c1 |
Quadratic twists by: -4 8 -19 |