Cremona's table of elliptic curves

2596 = 2² · 11 · 59

Field	Data	Notes
Atkin-Lehner	2- 11+ 59+	Signs for the Atkin-Lehner involutions
Class	2596a	Isogeny class
Conductor	2596	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1827584 = 28 · 112 · 59	Discriminant
Eigenvalues	2-  0 -2  2 11+  0 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-311,2110]	[a1,a2,a3,a4,a6]
j	12994659792/7139	j-invariant
L	1.3040686785374	L(r)(E,1)/r!
Ω	2.6081373570748	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10384f2 41536j2 23364b2 64900a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2596a2

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
-	0	-2	2	+	0	-2	-2	8	6	-8	6	2	12	8	-6	+	-8	12	12	-4	10	4	-6	-2

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Quadratic twists for elliptic curve 2596a2

-4	8	-3	5	-7	-11
10384f2	41536j2	23364b2	64900a2	127204d2	28556a2

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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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