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	12992be	Isogeny class
Conductor	12992	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-1543241728 = -1 · 218 · 7 · 292	Discriminant
Eigenvalues	2-  2 -2 7+ -4  2  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-609,-5887]	[a1,a2,a3,a4,a6]
Generators	[9309:172144:27]	Generators of the group modulo torsion
j	-95443993/5887	j-invariant
L	5.4608597859194	L(r)(E,1)/r!
Ω	0.47874901288635	Real period
R	5.7032595774936	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	12992u1 3248h1 116928dk1 90944ej1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992be1

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	2	4	2	0	-	2	-2	0	0	10	-6	12	4	12	8	-4	-12	-16	12	12

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Quadratic twists for elliptic curve 12992be1

-4	8	-3	-7
12992u1	3248h1	116928dk1	90944ej1

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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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