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	12696j	Isogeny class
Conductor	12696	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	5632	Modular degree for the optimal curve
Δ	-7105722672 = -1 · 24 · 3 · 236	Discriminant
Eigenvalues	2- 3+  2  0 -4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,353,-3272]	[a1,a2,a3,a4,a6]
Generators	[1245:4207:125]	Generators of the group modulo torsion
j	2048/3	j-invariant
L	4.2674607235301	L(r)(E,1)/r!
Ω	0.70300649496051	Real period
R	6.0703005649611	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	25392g1 101568bg1 38088i1 24a4	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 12696j1

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	0	-4	-2	-2	4	-	6	8	-6	-6	-4	0	2	4	2	4	8	10	8	4	6	-2

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Quadratic twists for elliptic curve 12696j1

-4	8	-3	-23
25392g1	101568bg1	38088i1	24a4

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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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