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	2574p	Isogeny class
Conductor	2574	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3120	Modular degree for the optimal curve
Δ	-9393905664 = -1 · 213 · 36 · 112 · 13	Discriminant
Eigenvalues	2+ 3-  3 -5 11- 13- -7  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,117,-4667]	[a1,a2,a3,a4,a6]
j	241804367/12886016	j-invariant
L	1.2395463665058	L(r)(E,1)/r!
Ω	0.61977318325292	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	20592bi1 82368ba1 286b1 64350ep1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574p1

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	-	-	-7	0	4	8	0	-3	8	-5	3	-2	14	8	0	5	16	-6	4	0	0

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Quadratic twists for elliptic curve 2574p1

-4	8	-3	5	-7	-11	13
20592bi1	82368ba1	286b1	64350ep1	126126cr1	28314bw1	33462co1

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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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