Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13-	Signs for the Atkin-Lehner involutions
Class	2704n	Isogeny class
Conductor	2704	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-294876348416 = -1 · 227 · 133	Discriminant
Eigenvalues	2-  1 -3  3  0 13- -3  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5152,-146444]	[a1,a2,a3,a4,a6]
Generators	[108:754:1]	Generators of the group modulo torsion
j	-1680914269/32768	j-invariant
L	3.4159633193442	L(r)(E,1)/r!
Ω	0.28142764291163	Real period
R	3.0344951938649	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	338e2 10816bn2 24336cg2 67600cr2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704n2

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	3	0	-	-3	6	-6	0	0	-3	0	-1	3	-6	-6	-8	12	-15	-6	-10	-6	6	-12

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Quadratic twists for elliptic curve 2704n2

-4	8	-3	5	13
338e2	10816bn2	24336cg2	67600cr2	2704m2

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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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