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	2574n	Isogeny class
Conductor	2574	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	21120	Modular degree for the optimal curve
Δ	-4445232241342464 = -1 · 211 · 312 · 11 · 135	Discriminant
Eigenvalues	2+ 3-  3  1 11- 13-  8 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5148,-3209648]	[a1,a2,a3,a4,a6]
j	-20699471212993/6097712265216	j-invariant
L	1.951301954272	L(r)(E,1)/r!
Ω	0.1951301954272	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	20592bh1 82368y1 858f1 64350ef1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574n1

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	1	-	-	8	-6	1	-1	0	6	11	-11	12	-2	-7	11	9	2	-11	6	-14	0	6

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Quadratic twists for elliptic curve 2574n1

-4	8	-3	5	-7	-11	13
20592bh1	82368y1	858f1	64350ef1	126126cs1	28314bv1	33462cn1

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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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