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
Δ	-11341398016 = -1 · 226 · 132	Discriminant
Eigenvalues	2-  0  1  4  4 13+  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6227,189202]	[a1,a2,a3,a4,a6]
j	-38575685889/16384	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	338a2 10816z2 24336bo2 67600bk2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704d2

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 2704d2

-4	8	-3	5	13
338a2	10816z2	24336bo2	67600bk2	2704e2

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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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