Cremona's table of elliptic curves

3596 = 2² · 29 · 31

Field	Data	Notes
Atkin-Lehner	2- 29+ 31-	Signs for the Atkin-Lehner involutions
Class	3596a	Isogeny class
Conductor	3596	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	1080	Modular degree for the optimal curve
Δ	-400867696 = -1 · 24 · 292 · 313	Discriminant
Eigenvalues	2- -2 -3 -1  0 -4  0  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-62,961]	[a1,a2,a3,a4,a6]
Generators	[6:29:1]	Generators of the group modulo torsion
j	-1674035968/25054231	j-invariant
L	1.7735898292656	L(r)(E,1)/r!
Ω	1.425261098983	Real period
R	0.62219821706043	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	14384c1 57536n1 32364q1 89900d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3596a1

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
-	-2	-3	-1	0	-4	0	5	6	+	-	8	-3	-4	0	6	9	8	-4	-15	2	-10	6	0	-1

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Quadratic twists for elliptic curve 3596a1

-4	8	-3	5	29	-31
14384c1	57536n1	32364q1	89900d1	104284b1	111476e1

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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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