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	2574m	Isogeny class
Conductor	2574	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1412930444766984 = 23 · 39 · 11 · 138	Discriminant
Eigenvalues	2+ 3- -2  4 11- 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-119403,15807325]	[a1,a2,a3,a4,a6]
Generators	[225:430:1]	Generators of the group modulo torsion
j	258252149810350513/1938176193096	j-invariant
L	2.4051396830572	L(r)(E,1)/r!
Ω	0.48232038313172	Real period
R	4.9866017841514	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20592bc3 82368bh4 858e3 64350es4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574m3

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	-	+	-2	-4	-4	2	0	-2	-10	-4	4	-2	4	10	-4	-12	2	-4	12	-2	2

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Quadratic twists for elliptic curve 2574m3

-4	8	-3	5	-7	-11	13
20592bc3	82368bh4	858e3	64350es4	126126dc4	28314ch4	33462cj4

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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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