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	8	Product of Tamagawa factors cp
Δ	6296309368832 = 211 · 72 · 894	Discriminant
Eigenvalues	2+ -2 -4 7-  0  4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-9768,350582]	[a1,a2,a3,a4,a6]
Generators	[-110:366:1]	Generators of the group modulo torsion
j	103056823169347321/6296309368832	j-invariant
L	1.1600097887795	L(r)(E,1)/r!
Ω	0.74082650457073	Real period
R	0.78291596049987	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	9968i2 39872v2 11214r2 31150q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1246g2

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 1246g2

-4	8	-3	5	-7	89
9968i2	39872v2	11214r2	31150q2	8722g2	110894d2

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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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