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	3640c	Isogeny class
Conductor	3640	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-910000 = -1 · 24 · 54 · 7 · 13	Discriminant
Eigenvalues	2+  0 5+ 7-  0 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,22,-23]	[a1,a2,a3,a4,a6]
j	73598976/56875	j-invariant
L	1.5601946047955	L(r)(E,1)/r!
Ω	1.5601946047955	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	7280a1 29120bc1 32760bn1 18200m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3640c1

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
+	0	+	-	0	+	6	4	0	-2	-8	2	6	-4	-8	-10	4	14	4	12	-10	8	12	14	-2

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Quadratic twists for elliptic curve 3640c1

-4	8	-3	5	-7	13
7280a1	29120bc1	32760bn1	18200m1	25480e1	47320x1

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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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