Cremona's table of elliptic curves

2664 = 2³ · 3² · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 37-	Signs for the Atkin-Lehner involutions
Class	2664b	Isogeny class
Conductor	2664	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-431136432 = -1 · 24 · 39 · 372	Discriminant
Eigenvalues	2+ 3-  0  0  0 -6  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-30,1001]	[a1,a2,a3,a4,a6]
Generators	[-8:27:1]	Generators of the group modulo torsion
j	-256000/36963	j-invariant
L	3.2342570633817	L(r)(E,1)/r!
Ω	1.3713116942624	Real period
R	0.5896283603709	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	5328d1 21312i1 888c1 66600bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2664b1

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

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Quadratic twists for elliptic curve 2664b1

-4	8	-3	5	37
5328d1	21312i1	888c1	66600bj1	98568p1

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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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