Cremona's table of elliptic curves

Curve 85905h1

85905 = 32 · 5 · 23 · 83



Data for elliptic curve 85905h1

Field Data Notes
Atkin-Lehner 3- 5- 23- 83+ Signs for the Atkin-Lehner involutions
Class 85905h Isogeny class
Conductor 85905 Conductor
∏ cp 96 Product of Tamagawa factors cp
deg 2045952 Modular degree for the optimal curve
Δ 793703408765625 = 37 · 56 · 234 · 83 Discriminant
Eigenvalues -1 3- 5-  0  2 -4 -8  2 Hecke eigenvalues for primes up to 20
Equation [1,-1,1,-13064702,18179226204] [a1,a2,a3,a4,a6]
Generators [2312:-19269:1] [-448:154956:1] Generators of the group modulo torsion
j 338294297402779752971929/1088756390625 j-invariant
L 7.7185958613715 L(r)(E,1)/r!
Ω 0.33444127631857 Real period
R 0.96162819501068 Regulator
r 2 Rank of the group of rational points
S 1.0000000000223 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 28635a1 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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