Cremona's table of elliptic curves

12740 = 2² · 5 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	12740b	Isogeny class
Conductor	12740	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	44352	Modular degree for the optimal curve
Δ	-210750056142080 = -1 · 28 · 5 · 78 · 134	Discriminant
Eigenvalues	2- -1 5+ 7+ -2 13- -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-18636,-1196600]	[a1,a2,a3,a4,a6]
Generators	[229:2548:1]	Generators of the group modulo torsion
j	-485043664/142805	j-invariant
L	2.9509158016677	L(r)(E,1)/r!
Ω	0.20124949647163	Real period
R	1.2219143622734	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	50960p1 114660bn1 63700a1 12740d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12740b1

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	-	-6	-8	5	-5	6	8	9	11	0	4	-12	15	-5	12	-2	-8	9	9	-18

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Quadratic twists for elliptic curve 12740b1

-4	-3	5	-7
50960p1	114660bn1	63700a1	12740d1

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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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