Cremona's table of elliptic curves

Curve 2112z1

2112 = 26 · 3 · 11



Data for elliptic curve 2112z1

Field Data Notes
Atkin-Lehner 2- 3- 11+ Signs for the Atkin-Lehner involutions
Class 2112z Isogeny class
Conductor 2112 Conductor
∏ cp 28 Product of Tamagawa factors cp
deg 5376 Modular degree for the optimal curve
Δ 1576599552 = 216 · 37 · 11 Discriminant
Eigenvalues 2- 3- -4  2 11+  0 -6  4 Hecke eigenvalues for primes up to 20
Equation [0,1,0,-32065,2199359] [a1,a2,a3,a4,a6]
Generators [119:-288:1] Generators of the group modulo torsion
j 55635379958596/24057 j-invariant
L 3.0550931895174 L(r)(E,1)/r!
Ω 1.2243143160063 Real period
R 0.35647862522789 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 2112j1 528c1 6336cn1 52800ei1 Quadratic twists by: -4 8 -3 5


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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