Cremona's table of elliptic curves

1274 = 2 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 7- 13+	Signs for the Atkin-Lehner involutions
Class	1274j	Isogeny class
Conductor	1274	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-3709888 = -1 · 26 · 73 · 132	Discriminant
Eigenvalues	2- -2 -2 7-  4 13+  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,6,-92]	[a1,a2,a3,a4,a6]
Generators	[6:10:1]	Generators of the group modulo torsion
j	68921/10816	j-invariant
L	2.6372692067043	L(r)(E,1)/r!
Ω	1.1759026245305	Real period
R	0.37379359363159	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	10192y1 40768br1 11466p1 31850bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274j1

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	+	4	-2	-8	-6	-4	-2	0	-4	-12	-2	-2	-10	4	-8	4	4	14	-12	8

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Quadratic twists for elliptic curve 1274j1

-4	8	-3	5	-7	13
10192y1	40768br1	11466p1	31850bb1	1274m1	16562q1

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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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