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	1274c	Isogeny class
Conductor	1274	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-2067798824 = -1 · 23 · 76 · 133	Discriminant
Eigenvalues	2+ -1  3 7-  6 13+  3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-221,2437]	[a1,a2,a3,a4,a6]
j	-10218313/17576	j-invariant
L	1.3150682261333	L(r)(E,1)/r!
Ω	1.3150682261333	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	10192u2 40768bl2 11466cd2 31850bz2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274c2

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	3	-	6	+	3	-2	0	6	4	-7	0	-1	-3	0	6	-8	14	-3	-2	8	-12	6	10

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Quadratic twists for elliptic curve 1274c2

-4	8	-3	5	-7	13
10192u2	40768bl2	11466cd2	31850bz2	26a1	16562bm2

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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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