Cremona's table of elliptic curves

2574 = 2 · 3² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	2574j	Isogeny class
Conductor	2574	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	43469748036 = 22 · 312 · 112 · 132	Discriminant
Eigenvalues	2+ 3-  2  0 11+ 13- -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-23166,-1351328]	[a1,a2,a3,a4,a6]
Generators	[419:7688:1]	Generators of the group modulo torsion
j	1886079023633377/59629284	j-invariant
L	2.694329416943	L(r)(E,1)/r!
Ω	0.38697841078426	Real period
R	3.4812399630804	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	20592bt2 82368bv2 858h2 64350dk2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574j2

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	0	+	-	-6	0	-4	-6	4	2	-10	-4	-8	6	-4	-2	-4	8	14	-8	-4	6	2

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Quadratic twists for elliptic curve 2574j2

-4	8	-3	5	-7	-11	13
20592bt2	82368bv2	858h2	64350dk2	126126by2	28314bt2	33462da2

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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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