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	2574u	Isogeny class
Conductor	2574	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	24393798 = 2 · 38 · 11 · 132	Discriminant
Eigenvalues	2- 3-  2  4 11+ 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1049,13331]	[a1,a2,a3,a4,a6]
j	174958262857/33462	j-invariant
L	4.1311367084701	L(r)(E,1)/r!
Ω	2.065568354235	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20592bv2 82368bx2 858c2 64350bb2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574u2

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

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Quadratic twists for elliptic curve 2574u2

-4	8	-3	5	-7	-11	13
20592bv2	82368bx2	858c2	64350bb2	126126eu2	28314r2	33462bh2

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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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