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	32	Product of Tamagawa factors cp
Δ	117542198689344 = 26 · 312 · 112 · 134	Discriminant
Eigenvalues	2+ 3- -2  4 11- 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-12483,-123755]	[a1,a2,a3,a4,a6]
Generators	[-18:317:1]	Generators of the group modulo torsion
j	295102348042033/161237583936	j-invariant
L	2.4051396830572	L(r)(E,1)/r!
Ω	0.48232038313172	Real period
R	2.4933008920757	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	20592bc2 82368bh2 858e2 64350es2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574m2

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 2574m2

-4	8	-3	5	-7	-11	13
20592bc2	82368bh2	858e2	64350es2	126126dc2	28314ch2	33462cj2

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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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