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	1274g	Isogeny class
Conductor	1274	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	-39139296140672 = -1 · 27 · 77 · 135	Discriminant
Eigenvalues	2+ -3  0 7- -5 13-  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1087,-301043]	[a1,a2,a3,a4,a6]
Generators	[261:4010:1]	Generators of the group modulo torsion
j	-1207949625/332678528	j-invariant
L	1.2248508907631	L(r)(E,1)/r!
Ω	0.28930268555327	Real period
R	0.21169020405404	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	10192bl1 40768ba1 11466cg1 31850bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274g1

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
+	-3	0	-	-5	-	4	-2	5	4	-1	7	9	-12	7	-4	6	-13	11	0	-7	-17	-4	-14	-5

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Quadratic twists for elliptic curve 1274g1

-4	8	-3	5	-7	13
10192bl1	40768ba1	11466cg1	31850bu1	182e1	16562br1

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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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