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	3640b	Isogeny class
Conductor	3640	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	6751996160 = 28 · 5 · 74 · 133	Discriminant
Eigenvalues	2+  2 5+ 7+ -2 13+  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3596,84116]	[a1,a2,a3,a4,a6]
Generators	[25:96:1]	Generators of the group modulo torsion
j	20093868785104/26374985	j-invariant
L	4.3821465966527	L(r)(E,1)/r!
Ω	1.3288892858763	Real period
R	3.2976009688897	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7280d1 29120u1 32760bk1 18200u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3640b1

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	+	+	-2	+	6	-6	6	-6	-6	6	-10	-6	0	6	-10	2	8	-10	-14	-12	12	-10	-2

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Quadratic twists for elliptic curve 3640b1

-4	8	-3	5	-7	13
7280d1	29120u1	32760bk1	18200u1	25480h1	47320bh1

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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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