Atkin-Lehner |
2+ 3+ 5+ 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
30030b |
Isogeny class |
Conductor |
30030 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-6808957515360000 = -1 · 28 · 33 · 54 · 72 · 114 · 133 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7- 11+ 13- 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,44422,-1647468] |
[a1,a2,a3,a4,a6] |
Generators |
[61:1107:1] |
Generators of the group modulo torsion |
j |
9693994288141282391/6808957515360000 |
j-invariant |
L |
3.3350995389319 |
L(r)(E,1)/r! |
Ω |
0.23747129660035 |
Real period |
R |
1.1703518090668 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
90090ea1 |
Quadratic twists by: -3 |