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	2640r	Isogeny class
Conductor	2640	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	-11384841600000000 = -1 · 213 · 35 · 58 · 114	Discriminant
Eigenvalues	2- 3- 5+  0 11+  2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,16264,5076564]	[a1,a2,a3,a4,a6]
Generators	[-20:2178:1]	Generators of the group modulo torsion
j	116149984977671/2779502343750	j-invariant
L	3.6096736150973	L(r)(E,1)/r!
Ω	0.30235685182386	Real period
R	1.1938454820267	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	330a4 10560bx4 7920bj4 13200bg4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640r4

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

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Quadratic twists for elliptic curve 2640r4

-4	8	-3	5	-7	-11
330a4	10560bx4	7920bj4	13200bg4	129360ex3	29040cu3

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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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