Cremona's table of elliptic curves

2704 = 2⁴ · 13²

Field	Data	Notes
Atkin-Lehner	2- 13-	Signs for the Atkin-Lehner involutions
Class	2704m	Isogeny class
Conductor	2704	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1423311812421484544 = -1 · 227 · 139	Discriminant
Eigenvalues	2-  1  3 -3  0 13- -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-870744,-318254572]	[a1,a2,a3,a4,a6]
Generators	[31310894:636673024:24389]	Generators of the group modulo torsion
j	-1680914269/32768	j-invariant
L	4.0031162609388	L(r)(E,1)/r!
Ω	0.078053984373142	Real period
R	6.410813447078	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	338d2 10816bo2 24336ch2 67600cq2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2704m2

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 2704m2

-4	8	-3	5	13
338d2	10816bo2	24336ch2	67600cq2	2704n2

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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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