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	12696r	Isogeny class
Conductor	12696	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-112131072 = -1 · 210 · 32 · 233	Discriminant
Eigenvalues	2- 3-  2 -4 -2  6  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,8,512]	[a1,a2,a3,a4,a6]
j	4/9	j-invariant
L	2.9402634476466	L(r)(E,1)/r!
Ω	1.4701317238233	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25392b1 101568o1 38088o1 12696t1	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 12696r1

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	-4	-2	6	0	6	-	6	-4	2	6	2	4	-14	-4	-10	-2	4	2	12	-6	12	12

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Quadratic twists for elliptic curve 12696r1

-4	8	-3	-23
25392b1	101568o1	38088o1	12696t1

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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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