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	40	Product of Tamagawa factors cp
Δ	8806460737499708192 = 25 · 718 · 132	Discriminant
Eigenvalues	2-  0 -2 7-  4 13-  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1533391,717149815]	[a1,a2,a3,a4,a6]
j	3389174547561866673/74853681183008	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	2	Number of elements in the torsion subgroup
Twists	10192bf3 40768m3 11466z3 31850e3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274k4

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 1274k4

-4	8	-3	5	-7	13
10192bf3	40768m3	11466z3	31850e3	182a3	16562e4

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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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