Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	2704c	Isogeny class
Conductor	2704	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	2704 = 24 · 132	Discriminant
Eigenvalues	2+ -1 -2 -1  1 13+  3  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4,-1]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	3328	j-invariant
L	2.354251918773	L(r)(E,1)/r!
Ω	3.385899007066	Real period
R	0.69531073249967	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1352b1 10816bd1 24336g1 67600c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704c1

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	-2	-1	1	+	3	7	-1	3	8	1	-11	-11	12	-6	-9	-9	-3	-5	2	12	-4	1	1

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Quadratic twists for elliptic curve 2704c1

-4	8	-3	5	13
1352b1	10816bd1	24336g1	67600c1	2704b1

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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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