Atkin-Lehner |
2+ 3- 5+ 7- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
30030q |
Isogeny class |
Conductor |
30030 |
Conductor |
∏ cp |
432 |
Product of Tamagawa factors cp |
deg |
497664 |
Modular degree for the optimal curve |
Δ |
-293745855166283520 = -1 · 28 · 36 · 5 · 72 · 113 · 136 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- 11- 13- -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,19051,-26054944] |
[a1,a2,a3,a4,a6] |
Generators |
[2382:18461:8] |
Generators of the group modulo torsion |
j |
764732966940509111/293745855166283520 |
j-invariant |
L |
4.9753807722065 |
L(r)(E,1)/r! |
Ω |
0.14416905763896 |
Real period |
R |
2.8758949468121 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
6 |
Number of elements in the torsion subgroup |
Twists |
90090du1 |
Quadratic twists by: -3 |