Atkin-Lehner |
2- 3- 5+ 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
30030bt |
Isogeny class |
Conductor |
30030 |
Conductor |
∏ cp |
3456 |
Product of Tamagawa factors cp |
deg |
774144 |
Modular degree for the optimal curve |
Δ |
-3157693080314572800 = -1 · 212 · 312 · 52 · 74 · 11 · 133 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7- 11+ 13- -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-749461,263897441] |
[a1,a2,a3,a4,a6] |
Generators |
[-880:16001:1] |
Generators of the group modulo torsion |
j |
-46555485820017544148689/3157693080314572800 |
j-invariant |
L |
9.7380353307345 |
L(r)(E,1)/r! |
Ω |
0.24815751400089 |
Real period |
R |
1.6350561607918 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
12 |
Number of elements in the torsion subgroup |
Twists |
90090cd1 |
Quadratic twists by: -3 |