Cremona's table of elliptic curves

Curve 12144u2

12144 = 24 · 3 · 11 · 23



Data for elliptic curve 12144u2

Field Data Notes
Atkin-Lehner 2- 3+ 11+ 23- Signs for the Atkin-Lehner involutions
Class 12144u Isogeny class
Conductor 12144 Conductor
∏ cp 4 Product of Tamagawa factors cp
Δ 442430208 = 28 · 33 · 112 · 232 Discriminant
Eigenvalues 2- 3+  2 -2 11+  6  4 -6 Hecke eigenvalues for primes up to 20
Equation [0,-1,0,-76172,-8066388] [a1,a2,a3,a4,a6]
Generators [2511389530:-82122433271:2197000] Generators of the group modulo torsion
j 190930594365830608/1728243 j-invariant
L 4.4080762190207 L(r)(E,1)/r!
Ω 0.28737583098959 Real period
R 15.339063844866 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 3036g2 48576dy2 36432cf2 Quadratic twists by: -4 8 -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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