Atkin-Lehner |
2- 3+ 5+ 13+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
127920z |
Isogeny class |
Conductor |
127920 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
7787520 |
Modular degree for the optimal curve |
Δ |
-497057786986475520 = -1 · 212 · 313 · 5 · 135 · 41 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 0 6 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-37858101,-89644831875] |
[a1,a2,a3,a4,a6] |
Generators |
[47063837176609101303633116102618304846946776905469835975093234311004840401031314973011867652008467055989527854440581332123179203718684:3001788621103414385068992563641552381301446962787268493605522619951017391583083550361926064987453439384668580811187875305728693938216573:5101341195133171518913404010065172817428915367079938420006649261509127592226060911129899174849924257628220919172684984827276567239] |
Generators of the group modulo torsion |
j |
-1465008863451482304446464/121351998775995 |
j-invariant |
L |
6.3470138592046 |
L(r)(E,1)/r! |
Ω |
0.030431954751548 |
Real period |
R |
208.56411988723 |
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 |
7995g1 |
Quadratic twists by: -4 |