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	2640o	Isogeny class
Conductor	2640	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-9702990000 = -1 · 24 · 36 · 54 · 113	Discriminant
Eigenvalues	2- 3+ 5+ -2 11+  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,219,4500]	[a1,a2,a3,a4,a6]
j	72268906496/606436875	j-invariant
L	0.94484196459386	L(r)(E,1)/r!
Ω	0.94484196459386	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	660d1 10560cn1 7920bl1 13200cc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640o1

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

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Quadratic twists for elliptic curve 2640o1

-4	8	-3	5	-7	-11
660d1	10560cn1	7920bl1	13200cc1	129360hn1	29040ce1

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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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