Cremona's table of elliptic curves

3640 = 2³ · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	3640a	Isogeny class
Conductor	3640	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	12480	Modular degree for the optimal curve
Δ	-83169632000000 = -1 · 211 · 56 · 7 · 135	Discriminant
Eigenvalues	2+ -1 5+ 7+  5 13+ -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-23416,1455116]	[a1,a2,a3,a4,a6]
Generators	[61:500:1]	Generators of the group modulo torsion
j	-693346671296498/40610171875	j-invariant
L	2.7022342576079	L(r)(E,1)/r!
Ω	0.59914293421815	Real period
R	2.2550831389961	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	7280c1 29120t1 32760bl1 18200t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3640a1

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	+	+	5	+	-2	-6	9	6	-5	1	3	6	-7	-12	-12	1	-9	8	5	-3	-2	14	-13

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Quadratic twists for elliptic curve 3640a1

-4	8	-3	5	-7	13
7280c1	29120t1	32760bl1	18200t1	25480g1	47320bg1

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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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