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	1274f	Isogeny class
Conductor	1274	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-35672 = -1 · 23 · 73 · 13	Discriminant
Eigenvalues	2+ -1  2 7-  1 13- -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4,8]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	-29791/104	j-invariant
L	1.8845561664655	L(r)(E,1)/r!
Ω	3.210852504534	Real period
R	0.2934666360109	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	10192bi1 40768q1 11466cl1 31850bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1274f1

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	2	-	1	-	-4	-4	-5	6	-11	7	-3	2	-3	-2	-4	-5	1	-2	-7	1	10	-6	-17

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Quadratic twists for elliptic curve 1274f1

-4	8	-3	5	-7	13
10192bi1	40768q1	11466cl1	31850bt1	1274b1	16562bj1

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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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