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	2574s	Isogeny class
Conductor	2574	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	4275640512 = 26 · 33 · 114 · 132	Discriminant
Eigenvalues	2- 3+ -2 -2 11- 13+  4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-926,10605]	[a1,a2,a3,a4,a6]
Generators	[-21:153:1]	Generators of the group modulo torsion
j	3249025693731/158357056	j-invariant
L	4.0936154643347	L(r)(E,1)/r!
Ω	1.3667213733725	Real period
R	0.12480035385198	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	20592p2 82368c2 2574a2 64350n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574s2

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	-2	-	+	4	2	-4	-4	-6	-2	2	-4	-8	4	4	-14	2	0	-10	-16	-12	10	14

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Quadratic twists for elliptic curve 2574s2

-4	8	-3	5	-7	-11	13
20592p2	82368c2	2574a2	64350n2	126126ee2	28314h2	33462g2

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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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