Cremona's table of elliptic curves

Curve 86112w1

86112 = 25 · 32 · 13 · 23



Data for elliptic curve 86112w1

Field Data Notes
Atkin-Lehner 2- 3+ 13- 23- Signs for the Atkin-Lehner involutions
Class 86112w Isogeny class
Conductor 86112 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 59392 Modular degree for the optimal curve
Δ 516672 = 26 · 33 · 13 · 23 Discriminant
Eigenvalues 2- 3+ -4 -4 -4 13-  2 -8 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-1197,15940] [a1,a2,a3,a4,a6]
Generators [21:8:1] [32:102:1] Generators of the group modulo torsion
j 109764631872/299 j-invariant
L 6.8029689016895 L(r)(E,1)/r!
Ω 2.5475847790327 Real period
R 2.6703601615436 Regulator
r 2 Rank of the group of rational points
S 0.99999999994202 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 86112d1 86112c1 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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