Cremona's table of elliptic curves

Curve 86112f2

86112 = 25 · 32 · 13 · 23



Data for elliptic curve 86112f2

Field Data Notes
Atkin-Lehner 2+ 3+ 13- 23- Signs for the Atkin-Lehner involutions
Class 86112f Isogeny class
Conductor 86112 Conductor
∏ cp 64 Product of Tamagawa factors cp
Δ 1218092647329792 = 212 · 39 · 134 · 232 Discriminant
Eigenvalues 2+ 3+ -2  2  4 13- -2 -6 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-140076,-20108736] [a1,a2,a3,a4,a6]
Generators [-218:260:1] Generators of the group modulo torsion
j 3770193726144/15108769 j-invariant
L 6.3935480354174 L(r)(E,1)/r!
Ω 0.24683873487232 Real period
R 1.6188575608573 Regulator
r 1 Rank of the group of rational points
S 0.9999999998826 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 86112b2 86112r2 Quadratic twists by: -4 -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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