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	2574l	Isogeny class
Conductor	2574	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-12210242616 = -1 · 23 · 36 · 115 · 13	Discriminant
Eigenvalues	2+ 3-  1  1 11- 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-594,7852]	[a1,a2,a3,a4,a6]
Generators	[17:41:1]	Generators of the group modulo torsion
j	-31824875809/16749304	j-invariant
L	2.6382106992478	L(r)(E,1)/r!
Ω	1.1792689906581	Real period
R	0.22371576969692	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	20592ba1 82368bf1 286e1 64350er1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574l1

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	1	-	+	-2	-4	-1	-7	-6	-2	5	5	-8	-2	-5	7	-7	0	5	-4	0	4	-16

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Quadratic twists for elliptic curve 2574l1

-4	8	-3	5	-7	-11	13
20592ba1	82368bf1	286e1	64350er1	126126cy1	28314ca1	33462cg1

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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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