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	160	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	-7151036224503808 = -1 · 220 · 79 · 132	Discriminant
Eigenvalues	2-  0 -2 7-  4 13-  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,42449,-2295625]	[a1,a2,a3,a4,a6]
j	71903073502287/60782804992	j-invariant
L	2.3143657556975	L(r)(E,1)/r!
Ω	0.23143657556975	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	10192bf1 40768m1 11466z1 31850e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274k1

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 1274k1

-4	8	-3	5	-7	13
10192bf1	40768m1	11466z1	31850e1	182a1	16562e1

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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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