Cremona's table of elliptic curves

Curve 27040b1

27040 = 25 · 5 · 132



Data for elliptic curve 27040b1

Field Data Notes
Atkin-Lehner 2+ 5+ 13+ Signs for the Atkin-Lehner involutions
Class 27040b Isogeny class
Conductor 27040 Conductor
∏ cp 16 Product of Tamagawa factors cp
deg 86016 Modular degree for the optimal curve
Δ 32629228840000 = 26 · 54 · 138 Discriminant
Eigenvalues 2+  0 5+  4  4 13+  2 -4 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-36673,-2689128] [a1,a2,a3,a4,a6]
Generators [-43622319100:-35918871702:381078125] Generators of the group modulo torsion
j 17657244864/105625 j-invariant
L 5.9921605159477 L(r)(E,1)/r!
Ω 0.3451194333679 Real period
R 17.362570567158 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 4 Number of elements in the torsion subgroup
Twists 27040c1 54080cu2 2080f1 Quadratic twists by: -4 8 13


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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