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	2574t	Isogeny class
Conductor	2574	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	9990198504 = 23 · 38 · 114 · 13	Discriminant
Eigenvalues	2- 3- -2  0 11+ 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-44951,3679431]	[a1,a2,a3,a4,a6]
Generators	[125:-18:1]	Generators of the group modulo torsion
j	13778603383488553/13703976	j-invariant
L	4.1984950971444	L(r)(E,1)/r!
Ω	1.0817019433008	Real period
R	1.2937929661513	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	20592bn3 82368ch4 858a3 64350bc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574t4

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

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Quadratic twists for elliptic curve 2574t4

-4	8	-3	5	-7	-11	13
20592bn3	82368ch4	858a3	64350bc4	126126ff4	28314ba4	33462bg4

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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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