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	3640i	Isogeny class
Conductor	3640	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	60569600 = 211 · 52 · 7 · 132	Discriminant
Eigenvalues	2-  2 5- 7+  0 13+ -8 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-320,-2068]	[a1,a2,a3,a4,a6]
Generators	[-249:100:27]	Generators of the group modulo torsion
j	1775007362/29575	j-invariant
L	4.8074723987396	L(r)(E,1)/r!
Ω	1.1296342329577	Real period
R	4.2557778956047	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	7280i2 29120e2 32760g2 18200g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3640i2

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	-	+	0	+	-8	-2	-6	-2	-4	2	-8	8	-8	0	-14	2	12	2	2	8	16	0	-2

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Quadratic twists for elliptic curve 3640i2

-4	8	-3	5	-7	13
7280i2	29120e2	32760g2	18200g2	25480m2	47320i2

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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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