Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	2704d	Isogeny class
Conductor	2704	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-2768896 = -1 · 214 · 132	Discriminant
Eigenvalues	2-  0  1  4  4 13+  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,13,-78]	[a1,a2,a3,a4,a6]
j	351/4	j-invariant
L	2.509934938963	L(r)(E,1)/r!
Ω	1.2549674694815	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	338a1 10816z1 24336bo1 67600bk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704d1

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	1	4	4	+	3	0	4	-1	4	-3	9	8	-8	-9	-4	7	4	-8	-11	4	0	6	-2

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Quadratic twists for elliptic curve 2704d1

-4	8	-3	5	13
338a1	10816z1	24336bo1	67600bk1	2704e1

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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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