Atkin-Lehner |
3+ 5- 7- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75075ba |
Isogeny class |
Conductor |
75075 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4291200 |
Modular degree for the optimal curve |
Δ |
-747307107421875 = -1 · 35 · 59 · 7 · 113 · 132 |
Discriminant |
Eigenvalues |
2 3+ 5- 7- 11+ 13+ -3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-34099458,-76631075557] |
[a1,a2,a3,a4,a6] |
Generators |
[188505006237378391719031500812766351546074916762869546:58195431363426804144560671642075607091346137515161932881:1970276991274266159888195467453243622950037972488] |
Generators of the group modulo torsion |
j |
-2245102192865634725888/382621239 |
j-invariant |
L |
10.238746984998 |
L(r)(E,1)/r! |
Ω |
0.031237961760029 |
Real period |
R |
81.941541702144 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75075bw1 |
Quadratic twists by: 5 |