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	2574w	Isogeny class
Conductor	2574	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-9173736 = -1 · 23 · 36 · 112 · 13	Discriminant
Eigenvalues	2- 3-  1  1 11- 13+  1 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-302,-1947]	[a1,a2,a3,a4,a6]
j	-4165509529/12584	j-invariant
L	3.4359980625225	L(r)(E,1)/r!
Ω	0.57266634375376	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20592z1 82368be1 286c1 64350bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574w1

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	-	+	1	-4	8	8	0	7	8	11	1	-2	-14	-8	8	-9	-4	2	0	4	8

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Quadratic twists for elliptic curve 2574w1

-4	8	-3	5	-7	-11	13
20592z1	82368be1	286c1	64350bt1	126126fv1	28314z1	33462t1

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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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