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	3640f	Isogeny class
Conductor	3640	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	37856000000 = 211 · 56 · 7 · 132	Discriminant
Eigenvalues	2+  2 5- 7+ -4 13+  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-840,812]	[a1,a2,a3,a4,a6]
j	32044133522/18484375	j-invariant
L	2.9445483191948	L(r)(E,1)/r!
Ω	0.98151610639825	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	7280j2 29120f2 32760be2 18200w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3640f2

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

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Quadratic twists for elliptic curve 3640f2

-4	8	-3	5	-7	13
7280j2	29120f2	32760be2	18200w2	25480d2	47320w2

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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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