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	2574i	Isogeny class
Conductor	2574	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-208494 = -1 · 2 · 36 · 11 · 13	Discriminant
Eigenvalues	2+ 3- -1 -3 11+ 13-  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,0,22]	[a1,a2,a3,a4,a6]
Generators	[-1:5:1]	Generators of the group modulo torsion
j	-1/286	j-invariant
L	2.109775789436	L(r)(E,1)/r!
Ω	2.5197318393454	Real period
R	0.41865085730394	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	20592br1 82368bo1 286f1 64350do1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574i1

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	-3	+	-	6	0	-1	3	10	2	-7	-1	4	-6	5	-11	-1	-16	-7	4	-4	-12	-16

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Quadratic twists for elliptic curve 2574i1

-4	8	-3	5	-7	-11	13
20592br1	82368bo1	286f1	64350do1	126126bv1	28314br1	33462cu1

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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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