Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	2704g	Isogeny class
Conductor	2704	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-131593177923584 = -1 · 221 · 137	Discriminant
Eigenvalues	2- -1  3 -1  6 13+ -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1242544,533523392]	[a1,a2,a3,a4,a6]
j	-10730978619193/6656	j-invariant
L	1.9299925129944	L(r)(E,1)/r!
Ω	0.48249812824861	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	338c3 10816bf3 24336by3 67600bn3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704g3

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
-	-1	3	-1	6	+	-3	2	0	6	-4	7	0	1	3	0	-6	8	14	-3	-2	-8	12	6	10

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Quadratic twists for elliptic curve 2704g3

-4	8	-3	5	13
338c3	10816bf3	24336by3	67600bn3	208a3

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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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