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	1274k	Isogeny class
Conductor	1274	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	1053365661857940704 = 25 · 79 · 138	Discriminant
Eigenvalues	2-  0 -2 7-  4 13-  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2897551,-1897063689]	[a1,a2,a3,a4,a6]
j	22868021811807457713/8953460393696	j-invariant
L	2.3143657556975	L(r)(E,1)/r!
Ω	0.11571828778488	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10192bf4 40768m4 11466z4 31850e4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274k3

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
-	0	-2	-	4	-	6	0	8	-10	8	6	6	4	8	6	-8	-10	4	-8	-2	8	0	-18	-2

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Quadratic twists for elliptic curve 1274k3

-4	8	-3	5	-7	13
10192bf4	40768m4	11466z4	31850e4	182a4	16562e3

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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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