Cremona's table of elliptic curves

12696 = 2³ · 3 · 23²

Field	Data	Notes
Atkin-Lehner	2- 3- 23-	Signs for the Atkin-Lehner involutions
Class	12696s	Isogeny class
Conductor	12696	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	3027538944 = 210 · 35 · 233	Discriminant
Eigenvalues	2- 3- -2 -2 -4 -6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-119224,15805376]	[a1,a2,a3,a4,a6]
Generators	[-376:2760:1] [176:552:1]	Generators of the group modulo torsion
j	15043017316604/243	j-invariant
L	6.3867465876279	L(r)(E,1)/r!
Ω	1.0160969965156	Real period
R	1.2571135648525	Regulator
r	2	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25392d2 101568i2 38088e2 12696p2	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 12696s2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	-2	-2	-4	-6	-6	-6	-	-6	8	-8	-6	10	4	2	8	-8	-10	-8	-10	-6	-12	-18	12

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Quadratic twists for elliptic curve 12696s2

-4	8	-3	-23
25392d2	101568i2	38088e2	12696p2

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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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