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	2640s	Isogeny class
Conductor	2640	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	464640 = 28 · 3 · 5 · 112	Discriminant
Eigenvalues	2- 3- 5+  0 11+ -4 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-76,-280]	[a1,a2,a3,a4,a6]
Generators	[122:387:8]	Generators of the group modulo torsion
j	192143824/1815	j-invariant
L	3.5655296431396	L(r)(E,1)/r!
Ω	1.616101468644	Real period
R	4.4125071504714	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	660b2 10560by2 7920bk2 13200bh2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640s2

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	+	-4	-2	-2	8	-4	4	-2	-12	-8	4	-10	-4	6	-12	0	-16	-6	2	18	-2

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Quadratic twists for elliptic curve 2640s2

-4	8	-3	5	-7	-11
660b2	10560by2	7920bk2	13200bh2	129360fa2	29040cv2

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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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