Cremona's table of elliptic curves

2738 = 2 · 37²

Field	Data	Notes
Atkin-Lehner	2- 37+	Signs for the Atkin-Lehner involutions
Class	2738d	Isogeny class
Conductor	2738	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-87616 = -1 · 26 · 372	Discriminant
Eigenvalues	2- -2 -3 -4 -6 -2 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-47,121]	[a1,a2,a3,a4,a6]
Generators	[70:549:1] [0:11:1]	Generators of the group modulo torsion
j	-8398297/64	j-invariant
L	3.4779513750643	L(r)(E,1)/r!
Ω	3.4195920188379	Real period
R	0.16951102918632	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21904j1 87616k1 24642h1 68450g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2738d1

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	-3	-4	-6	-2	-3	-2	-6	-3	-2	+	3	4	-6	-6	0	1	2	-12	-10	-14	6	-3	13

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Quadratic twists for elliptic curve 2738d1

-4	8	-3	5	37
21904j1	87616k1	24642h1	68450g1	2738b1

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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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