Atkin-Lehner |
3- 5+ 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
68355p |
Isogeny class |
Conductor |
68355 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
747461925 = 39 · 52 · 72 · 31 |
Discriminant |
Eigenvalues |
-2 3- 5+ 7- -1 2 5 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-3423,-77072] |
[a1,a2,a3,a4,a6] |
Generators |
[-34:2:1] |
Generators of the group modulo torsion |
j |
124171177984/20925 |
j-invariant |
L |
3.2508413557565 |
L(r)(E,1)/r! |
Ω |
0.62416903787373 |
Real period |
R |
1.3020676927657 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999987579 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22785h1 68355v1 |
Quadratic twists by: -3 -7 |