Cremona's table of elliptic curves

1246 = 2 · 7 · 89

Field	Data	Notes
Atkin-Lehner	2+ 7- 89-	Signs for the Atkin-Lehner involutions
Class	1246g	Isogeny class
Conductor	1246	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	-232561573888 = -1 · 222 · 7 · 892	Discriminant
Eigenvalues	2+ -2 -4 7-  0  4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,472,22902]	[a1,a2,a3,a4,a6]
Generators	[-22:55:1]	Generators of the group modulo torsion
j	11664649752839/232561573888	j-invariant
L	1.1600097887795	L(r)(E,1)/r!
Ω	0.74082650457073	Real period
R	1.5658319209997	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	9968i1 39872v1 11214r1 31150q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1246g1

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	-	0	4	-2	2	0	6	-4	-2	-2	4	-4	6	-14	-8	4	-8	-6	0	10	-	-10

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Quadratic twists for elliptic curve 1246g1

-4	8	-3	5	-7	89
9968i1	39872v1	11214r1	31150q1	8722g1	110894d1

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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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