Atkin-Lehner |
2+ 3+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68208h |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
16128 |
Modular degree for the optimal curve |
Δ |
3273984 = 28 · 32 · 72 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7- 2 -3 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-457,-3611] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:1:1] [28:69:1] |
Generators of the group modulo torsion |
j |
843308032/261 |
j-invariant |
L |
7.6765428937181 |
L(r)(E,1)/r! |
Ω |
1.0324033541096 |
Real period |
R |
3.717802186093 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000053 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34104q1 68208o1 |
Quadratic twists by: -4 -7 |