Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	2704j	Isogeny class
Conductor	2704	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-32898294480896 = -1 · 219 · 137	Discriminant
Eigenvalues	2-  3  1  1 -2 13+ -3  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7267,-364702]	[a1,a2,a3,a4,a6]
j	-2146689/1664	j-invariant
L	4.0028435166812	L(r)(E,1)/r!
Ω	0.25017771979257	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	338f1 10816bk1 24336bl1 67600cl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704j1

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
-	3	1	1	-2	+	-3	6	4	2	4	-3	0	5	13	12	-10	-8	-2	-5	10	4	0	-6	-14

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Quadratic twists for elliptic curve 2704j1

-4	8	-3	5	13
338f1	10816bk1	24336bl1	67600cl1	208d1

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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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