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	2574f	Isogeny class
Conductor	2574	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-9525420343296 = -1 · 214 · 37 · 112 · 133	Discriminant
Eigenvalues	2+ 3- -2  4 11+ 13+  8 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2988,162000]	[a1,a2,a3,a4,a6]
j	-4047806261953/13066420224	j-invariant
L	1.2776356243074	L(r)(E,1)/r!
Ω	0.63881781215372	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	20592bo1 82368cj1 858l1 64350eb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574f1

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	4	+	+	8	-6	6	2	-2	4	-2	4	-4	8	-12	-2	12	16	0	-8	-4	-10	10

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Quadratic twists for elliptic curve 2574f1

-4	8	-3	5	-7	-11	13
20592bo1	82368cj1	858l1	64350eb1	126126cg1	28314ci1	33462cz1

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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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