Cremona's table of elliptic curves

2738 = 2 · 37²

Field	Data	Notes
Atkin-Lehner	2+ 37+	Signs for the Atkin-Lehner involutions
Class	2738b	Isogeny class
Conductor	2738	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	21312	Modular degree for the optimal curve
Δ	-224798685050944 = -1 · 26 · 378	Discriminant
Eigenvalues	2+ -2  3 -4 -6  2  3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-64372,6322098]	[a1,a2,a3,a4,a6]
Generators	[124:438:1]	Generators of the group modulo torsion
j	-8398297/64	j-invariant
L	1.7683455207047	L(r)(E,1)/r!
Ω	0.56217746489443	Real period
R	4.7182935046234	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	21904i1 87616l1 24642t1 68450z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2738b1

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 2738b1

-4	8	-3	5	37
21904i1	87616l1	24642t1	68450z1	2738d1

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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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