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	8	Product of Tamagawa factors cp
Δ	183675444480 = 28 · 34 · 5 · 116	Discriminant
Eigenvalues	2+ 3+ 5+  2 11+  0 -8  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1716,-17424]	[a1,a2,a3,a4,a6]
Generators	[-12:36:1]	Generators of the group modulo torsion
j	2184181167184/717482205	j-invariant
L	2.7607346522813	L(r)(E,1)/r!
Ω	0.76120728689801	Real period
R	1.8133921599276	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	1320d2 10560cl2 7920q2 13200s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640a2

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 2640a2

-4	8	-3	5	-7	-11
1320d2	10560cl2	7920q2	13200s2	129360cm2	29040g2

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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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