Cremona's table of elliptic curves

7544 = 2³ · 23 · 41

Field	Data	Notes
Atkin-Lehner	2+ 23+ 41+	Signs for the Atkin-Lehner involutions
Class	7544a	Isogeny class
Conductor	7544	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	5146224933865472 = 211 · 232 · 416	Discriminant
Eigenvalues	2+  2 -2 -4 -2  4  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-45544,-1428180]	[a1,a2,a3,a4,a6]
Generators	[-23262069:141322094:132651]	Generators of the group modulo torsion
j	5101487277496274/2512805143489	j-invariant
L	4.6081602391261	L(r)(E,1)/r!
Ω	0.34366304872493	Real period
R	13.408948841673	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	15088a2 60352b2 67896h2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 7544a2

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

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Quadratic twists for elliptic curve 7544a2

-4	8	-3
15088a2	60352b2	67896h2

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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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