Cremona's table of elliptic curves

12992 = 2⁶ · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 7+ 29-	Signs for the Atkin-Lehner involutions
Class	12992z	Isogeny class
Conductor	12992	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-24113152 = -1 · 212 · 7 · 292	Discriminant
Eigenvalues	2-  0  4 7+ -4  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-68,-320]	[a1,a2,a3,a4,a6]
Generators	[60:460:1]	Generators of the group modulo torsion
j	-8489664/5887	j-invariant
L	5.6187946921661	L(r)(E,1)/r!
Ω	0.80650281662241	Real period
R	3.4834315369767	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	12992bj1 6496a1 116928dp1 90944dm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992z1

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
-	0	4	+	-4	4	0	-4	0	-	10	2	-12	-12	-6	-6	-6	10	-12	8	-4	0	6	-4	0

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Quadratic twists for elliptic curve 12992z1

-4	8	-3	-7
12992bj1	6496a1	116928dp1	90944dm1

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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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