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	2574o	Isogeny class
Conductor	2574	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-607968504 = -1 · 23 · 312 · 11 · 13	Discriminant
Eigenvalues	2+ 3-  3  5 11- 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,117,1053]	[a1,a2,a3,a4,a6]
j	241804367/833976	j-invariant
L	2.3077791570833	L(r)(E,1)/r!
Ω	1.1538895785417	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20592bj1 82368z1 858j1 64350eq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574o1

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
+	-	3	5	-	-	0	2	-3	3	8	-10	3	5	-12	6	9	-13	5	-6	-7	-10	-6	0	-10

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Quadratic twists for elliptic curve 2574o1

-4	8	-3	5	-7	-11	13
20592bj1	82368z1	858j1	64350eq1	126126cq1	28314bx1	33462cp1

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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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