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	2640a	Isogeny class
Conductor	2640	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-3493076400 = -1 · 24 · 38 · 52 · 113	Discriminant
Eigenvalues	2+ 3+ 5+  2 11+  0 -8  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,309,-2034]	[a1,a2,a3,a4,a6]
Generators	[330:5994:1]	Generators of the group modulo torsion
j	203269830656/218317275	j-invariant
L	2.7607346522813	L(r)(E,1)/r!
Ω	0.76120728689801	Real period
R	3.6267843198553	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	1320d1 10560cl1 7920q1 13200s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640a1

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

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Quadratic twists for elliptic curve 2640a1

-4	8	-3	5	-7	-11
1320d1	10560cl1	7920q1	13200s1	129360cm1	29040g1

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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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