Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	2704i	Isogeny class
Conductor	2704	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	3120	Modular degree for the optimal curve
Δ	-208827064576 = -1 · 28 · 138	Discriminant
Eigenvalues	2-  2 -3  4  0 13+  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-732,23516]	[a1,a2,a3,a4,a6]
j	-208	j-invariant
L	2.6060479107442	L(r)(E,1)/r!
Ω	0.86868263691474	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	676c1 10816bg1 24336bx1 67600cg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704i1

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	0	+	3	-2	6	9	-2	-7	3	4	6	9	0	5	-2	6	-1	4	-12	6	14

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Quadratic twists for elliptic curve 2704i1

-4	8	-3	5	13
676c1	10816bg1	24336bx1	67600cg1	2704h1

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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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