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	2541i	Isogeny class
Conductor	2541	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	36172479189 = 3 · 77 · 114	Discriminant
Eigenvalues	-2 3+ -3 7- 11- -2 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1492,20712]	[a1,a2,a3,a4,a6]
Generators	[15:-39:1]	Generators of the group modulo torsion
j	25104437248/2470629	j-invariant
L	1.1235237508615	L(r)(E,1)/r!
Ω	1.1254392722152	Real period
R	0.047537998996689	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	40656cr1 7623r1 63525bm1 17787be1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2541i1

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
-2	+	-3	-	-	-2	-3	4	2	-8	2	10	-2	-9	9	-8	-3	10	13	14	10	4	-1	-9	-16

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Quadratic twists for elliptic curve 2541i1

-4	-3	5	-7	-11
40656cr1	7623r1	63525bm1	17787be1	2541d1

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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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