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	1274d	Isogeny class
Conductor	1274	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	14784	Modular degree for the optimal curve
Δ	-2579573013075968 = -1 · 211 · 713 · 13	Discriminant
Eigenvalues	2+ -1 -4 7- -1 13+ -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-225817,-41469595]	[a1,a2,a3,a4,a6]
j	-10824513276632329/21926008832	j-invariant
L	0.21898150252865	L(r)(E,1)/r!
Ω	0.10949075126433	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10192v1 40768bm1 11466ce1 31850bw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274d1

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	-4	-	-1	+	-4	-2	-7	-8	-3	7	7	-8	-3	0	6	13	7	4	-9	-13	16	6	-11

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Quadratic twists for elliptic curve 1274d1

-4	8	-3	5	-7	13
10192v1	40768bm1	11466ce1	31850bw1	182c1	16562bn1

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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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