Atkin-Lehner |
3+ 5- 7- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
30135o |
Isogeny class |
Conductor |
30135 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
325248 |
Modular degree for the optimal curve |
Δ |
-15330111943426875 = -1 · 311 · 54 · 72 · 414 |
Discriminant |
Eigenvalues |
-2 3+ 5- 7- -2 -1 -4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,44000,4767258] |
[a1,a2,a3,a4,a6] |
Generators |
[174:4202:1] |
Generators of the group modulo torsion |
j |
192254180071632896/312859427416875 |
j-invariant |
L |
2.1276017495029 |
L(r)(E,1)/r! |
Ω |
0.2685170234239 |
Real period |
R |
0.99044081189601 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
90405ba1 30135x1 |
Quadratic twists by: -3 -7 |