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	2541j	Isogeny class
Conductor	2541	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	22869 = 33 · 7 · 112	Discriminant
Eigenvalues	0 3- -3 7+ 11-  4  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-7,-5]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	360448/189	j-invariant
L	2.6781999955075	L(r)(E,1)/r!
Ω	3.0751867343751	Real period
R	0.29030215364051	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40656bx1 7623e1 63525n1 17787g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2541j1

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	-	-3	+	-	4	3	-2	0	6	2	-10	-6	-11	-3	12	-3	-8	5	-12	-8	-8	-15	15	14

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Quadratic twists for elliptic curve 2541j1

-4	-3	5	-7	-11
40656bx1	7623e1	63525n1	17787g1	2541k1

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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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