Cremona's table of elliptic curves

Curve 83232bf1

83232 = 25 · 32 · 172



Data for elliptic curve 83232bf1

Field Data Notes
Atkin-Lehner 2- 3- 17+ Signs for the Atkin-Lehner involutions
Class 83232bf Isogeny class
Conductor 83232 Conductor
∏ cp 32 Product of Tamagawa factors cp
deg 442368 Modular degree for the optimal curve
Δ -33082147228299264 = -1 · 212 · 39 · 177 Discriminant
Eigenvalues 2- 3- -1 -2  1 -1 17+ -1 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-367608,86232976] [a1,a2,a3,a4,a6]
Generators [1088:31212:1] Generators of the group modulo torsion
j -76225024/459 j-invariant
L 5.2271212595719 L(r)(E,1)/r!
Ω 0.37092682915447 Real period
R 0.44037671731299 Regulator
r 1 Rank of the group of rational points
S 0.99999999984855 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 83232be1 27744i1 4896k1 Quadratic twists by: -4 -3 17


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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