Cremona's table of elliptic curves

Curve 52065c1

52065 = 32 · 5 · 13 · 89



Data for elliptic curve 52065c1

Field Data Notes
Atkin-Lehner 3+ 5- 13+ 89- Signs for the Atkin-Lehner involutions
Class 52065c Isogeny class
Conductor 52065 Conductor
∏ cp 24 Product of Tamagawa factors cp
deg 241920 Modular degree for the optimal curve
Δ -1240739375484375 = -1 · 33 · 56 · 135 · 892 Discriminant
Eigenvalues  1 3+ 5-  2  4 13+  2 -8 Hecke eigenvalues for primes up to 20
Equation [1,-1,0,12081,1612800] [a1,a2,a3,a4,a6]
Generators [678:14061:8] Generators of the group modulo torsion
j 7221848602724757/45953310203125 j-invariant
L 8.6237828339494 L(r)(E,1)/r!
Ω 0.35165163865964 Real period
R 4.0872755334707 Regulator
r 1 Rank of the group of rational points
S 0.99999999999522 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 52065a1 Quadratic twists by: -3


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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