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	12992h	Isogeny class
Conductor	12992	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-96452608 = -1 · 214 · 7 · 292	Discriminant
Eigenvalues	2+ -2 -2 7+  0 -6  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,111,-113]	[a1,a2,a3,a4,a6]
Generators	[2:11:1] [3:16:1]	Generators of the group modulo torsion
j	9148592/5887	j-invariant
L	4.2722823251946	L(r)(E,1)/r!
Ω	1.0862956744561	Real period
R	1.9664454280989	Regulator
r	2	Rank of the group of rational points
S	0.99999999999976	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12992bl2 1624c2 116928z2 90944bz2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992h2

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

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Quadratic twists for elliptic curve 12992h2

-4	8	-3	-7
12992bl2	1624c2	116928z2	90944bz2

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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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