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
deg	640	Modular degree for the optimal curve
Δ	-13760604 = -1 · 22 · 37 · 112 · 13	Discriminant
Eigenvalues	2- 3-  2  4 11+ 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-59,263]	[a1,a2,a3,a4,a6]
j	-30664297/18876	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	20592bv1 82368bx1 858c1 64350bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574u1

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 2574u1

-4	8	-3	5	-7	-11	13
20592bv1	82368bx1	858c1	64350bb1	126126eu1	28314r1	33462bh1

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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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