Cremona's table of elliptic curves

Curve 12075n1

12075 = 3 · 52 · 7 · 23



Data for elliptic curve 12075n1

Field Data Notes
Atkin-Lehner 3+ 5- 7+ 23- Signs for the Atkin-Lehner involutions
Class 12075n Isogeny class
Conductor 12075 Conductor
∏ cp 3 Product of Tamagawa factors cp
deg 14400 Modular degree for the optimal curve
Δ -748838671875 = -1 · 35 · 58 · 73 · 23 Discriminant
Eigenvalues  0 3+ 5- 7+  4  6 -4 -3 Hecke eigenvalues for primes up to 20
Equation [0,-1,1,167,-41682] [a1,a2,a3,a4,a6]
Generators [92:862:1] Generators of the group modulo torsion
j 1310720/1917027 j-invariant
L 3.2618142836786 L(r)(E,1)/r!
Ω 0.41839965648108 Real period
R 2.5986432136137 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 36225ca1 12075r1 84525db1 Quadratic twists by: -3 5 -7


Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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