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	-347488235454464 = -1 · 215 · 139	Discriminant
Eigenvalues	2- -1  3 -1  6 13+ -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-12224,1040896]	[a1,a2,a3,a4,a6]
j	-10218313/17576	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	338c2 10816bf2 24336by2 67600bn2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704g2

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 2704g2

-4	8	-3	5	13
338c2	10816bf2	24336by2	67600bn2	208a2

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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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