Atkin-Lehner |
3+ 5+ 7+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
30135b |
Isogeny class |
Conductor |
30135 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
336000 |
Modular degree for the optimal curve |
Δ |
43614484700653125 = 310 · 55 · 78 · 41 |
Discriminant |
Eigenvalues |
-2 3+ 5+ 7+ -4 5 -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-135256,16342962] |
[a1,a2,a3,a4,a6] |
Generators |
[-212:5953:1] |
Generators of the group modulo torsion |
j |
47469233803264/7565653125 |
j-invariant |
L |
1.841724232123 |
L(r)(E,1)/r! |
Ω |
0.34486751145517 |
Real period |
R |
0.89006365775651 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
90405bj1 30135bh1 |
Quadratic twists by: -3 -7 |