Cremona's table of elliptic curves

2541 = 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	3+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	2541c	Isogeny class
Conductor	2541	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-53361 = -1 · 32 · 72 · 112	Discriminant
Eigenvalues	-1 3+ -3 7+ 11- -7 -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,3,12]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1] [0:3:1]	Generators of the group modulo torsion
j	24167/441	j-invariant
L	2.0392135816	L(r)(E,1)/r!
Ω	2.643433638616	Real period
R	0.19285651357111	Regulator
r	2	Rank of the group of rational points
S	0.99999999999981	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40656do1 7623g1 63525bt1 17787v1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2541c1

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
-1	+	-3	+	-	-7	-3	2	-4	-7	-10	1	5	-6	-6	-5	-6	-10	-8	-10	-10	2	16	3	-19

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Quadratic twists for elliptic curve 2541c1

-4	-3	5	-7	-11
40656do1	7623g1	63525bt1	17787v1	2541f1

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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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