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	2574y	Isogeny class
Conductor	2574	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-563767776 = -1 · 25 · 36 · 11 · 133	Discriminant
Eigenvalues	2- 3- -3 -1 11- 13- -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-59,-1141]	[a1,a2,a3,a4,a6]
Generators	[39:-254:1]	Generators of the group modulo torsion
j	-30664297/773344	j-invariant
L	3.984878452189	L(r)(E,1)/r!
Ω	0.70975062163271	Real period
R	0.18714922916739	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	20592bk1 82368x1 286a1 64350bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574y1

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
-	-	-3	-1	-	-	-6	8	3	-9	2	-10	-9	-1	0	-6	3	-7	-7	-12	-1	-4	0	-12	-4

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Quadratic twists for elliptic curve 2574y1

-4	8	-3	5	-7	-11	13
20592bk1	82368x1	286a1	64350bl1	126126fs1	28314x1	33462x1

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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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