Cremona's table of elliptic curves

2640 = 2⁴ · 3 · 5 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	2640b	Isogeny class
Conductor	2640	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-222750000 = -1 · 24 · 34 · 56 · 11	Discriminant
Eigenvalues	2+ 3+ 5+ -2 11+  0  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-371,2970]	[a1,a2,a3,a4,a6]
Generators	[14:18:1]	Generators of the group modulo torsion
j	-353912203264/13921875	j-invariant
L	2.5020139218418	L(r)(E,1)/r!
Ω	1.7566307796354	Real period
R	1.4243254478105	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	1320l1 10560cm1 7920t1 13200r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640b1

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	4	4	-4	6	0	-2	2	2	-12	-2	-4	2	0	-8	0	-8	-2	-2	-2

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Quadratic twists for elliptic curve 2640b1

-4	8	-3	5	-7	-11
1320l1	10560cm1	7920t1	13200r1	129360ck1	29040e1

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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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