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	1274i	Isogeny class
Conductor	1274	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-21412118 = -1 · 2 · 77 · 13	Discriminant
Eigenvalues	2- -1  0 7- -3 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-767488,258474999]	[a1,a2,a3,a4,a6]
Generators	[4038:-1827:8]	Generators of the group modulo torsion
j	-424962187484640625/182	j-invariant
L	3.1574827618888	L(r)(E,1)/r!
Ω	0.90843259190521	Real period
R	0.86893699929534	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10192r3 40768bh3 11466n3 31850v3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274i3

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	0	-	-3	+	0	-2	-3	0	-5	-7	-3	8	3	-12	-6	1	5	12	-11	-1	-12	18	-17

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Quadratic twists for elliptic curve 1274i3

-4	8	-3	5	-7	13
10192r3	40768bh3	11466n3	31850v3	182b3	16562h3

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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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