Atkin-Lehner |
2+ 7- 13- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
85358i |
Isogeny class |
Conductor |
85358 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1212288 |
Modular degree for the optimal curve |
Δ |
-147421362166693888 = -1 · 222 · 79 · 13 · 67 |
Discriminant |
Eigenvalues |
2+ -2 0 7- 2 13- -2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-318526,71590320] |
[a1,a2,a3,a4,a6] |
Generators |
[49745:326297:125] |
Generators of the group modulo torsion |
j |
-88567432609375/3653238784 |
j-invariant |
L |
3.0873956228673 |
L(r)(E,1)/r! |
Ω |
0.32308436619874 |
Real period |
R |
2.3890010911994 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000030039 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85358e1 |
Quadratic twists by: -7 |