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	1274l	Isogeny class
Conductor	1274	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	6048	Modular degree for the optimal curve
Δ	-268593608192 = -1 · 29 · 79 · 13	Discriminant
Eigenvalues	2- -1  2 7- -5 13-  8  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-99177,-12063017]	[a1,a2,a3,a4,a6]
j	-2673465150439/6656	j-invariant
L	2.4212477750104	L(r)(E,1)/r!
Ω	0.13451376527836	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10192bj1 40768r1 11466bc1 31850j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274l1

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
-	-1	2	-	-5	-	8	8	7	6	-5	1	-9	2	3	10	-4	7	-5	-14	11	-11	-14	6	13

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Quadratic twists for elliptic curve 1274l1

-4	8	-3	5	-7	13
10192bj1	40768r1	11466bc1	31850j1	1274h1	16562k1

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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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