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	12740c	Isogeny class
Conductor	12740	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-1783600 = -1 · 24 · 52 · 73 · 13	Discriminant
Eigenvalues	2-  2 5+ 7- -6 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,19,50]	[a1,a2,a3,a4,a6]
j	131072/325	j-invariant
L	1.8482729190234	L(r)(E,1)/r!
Ω	1.8482729190234	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50960bf1 114660cb1 63700p1 12740e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12740c1

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
-	2	+	-	-6	-	-6	4	-8	-2	0	8	6	4	12	6	4	4	-16	2	6	-12	-12	-6	2

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Quadratic twists for elliptic curve 12740c1

-4	-3	5	-7
50960bf1	114660cb1	63700p1	12740e1

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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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