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	1274a	Isogeny class
Conductor	1274	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-19185257728 = -1 · 28 · 78 · 13	Discriminant
Eigenvalues	2+  0  0 7+  1 13+ -1  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-107,-6651]	[a1,a2,a3,a4,a6]
Generators	[86:741:1]	Generators of the group modulo torsion
j	-23625/3328	j-invariant
L	1.9763360721251	L(r)(E,1)/r!
Ω	0.54246944591944	Real period
R	0.60720349843095	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	10192l1 40768e1 11466br1 31850bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274a1

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	0	+	1	+	-1	5	2	-5	-8	-8	0	-6	11	5	-3	1	-7	-9	-2	-14	-8	-16	2

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Quadratic twists for elliptic curve 1274a1

-4	8	-3	5	-7	13
10192l1	40768e1	11466br1	31850bo1	1274e1	16562z1

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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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