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	2574x	Isogeny class
Conductor	2574	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	183931773874992 = 24 · 39 · 112 · 136	Discriminant
Eigenvalues	2- 3-  0 -4 11- 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-16205,-448315]	[a1,a2,a3,a4,a6]
Generators	[-39:370:1]	Generators of the group modulo torsion
j	645532578015625/252306960048	j-invariant
L	4.3193594937223	L(r)(E,1)/r!
Ω	0.43749823068009	Real period
R	0.2056846172368	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	20592bf2 82368s2 858b2 64350bn2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574x2

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
-	-	0	-4	-	-	0	-4	0	0	-10	2	6	-10	0	-6	0	2	2	-12	-10	-10	12	-12	-10

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Quadratic twists for elliptic curve 2574x2

-4	8	-3	5	-7	-11	13
20592bf2	82368s2	858b2	64350bn2	126126fl2	28314p2	33462r2

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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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