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	2574c	Isogeny class
Conductor	2574	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	1492940592 = 24 · 33 · 112 · 134	Discriminant
Eigenvalues	2+ 3+  0 -2 11- 13-  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-372,-1952]	[a1,a2,a3,a4,a6]
Generators	[-12:32:1]	Generators of the group modulo torsion
j	211176358875/55294096	j-invariant
L	2.3320379940585	L(r)(E,1)/r!
Ω	1.1080762332294	Real period
R	0.26307282885019	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20592s2 82368a2 2574r2 64350cx2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574c2

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

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Quadratic twists for elliptic curve 2574c2

-4	8	-3	5	-7	-11	13
20592s2	82368a2	2574r2	64350cx2	126126o2	28314be2	33462bo2

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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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