Cremona's table of elliptic curves

4576 = 2⁵ · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	4576b	Isogeny class
Conductor	4576	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-136108544 = -1 · 29 · 112 · 133	Discriminant
Eigenvalues	2+ -1  3  1 11+ 13+ -5  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-144,-824]	[a1,a2,a3,a4,a6]
Generators	[45:286:1]	Generators of the group modulo torsion
j	-649461896/265837	j-invariant
L	3.7159056722213	L(r)(E,1)/r!
Ω	0.6751208156686	Real period
R	2.7520301448129	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	4576f1 9152m1 41184bg1 114400u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4576b1

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	1	+	+	-5	0	4	-8	8	3	-12	-9	3	-6	-6	12	4	5	-4	-10	-16	-8	-8

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Quadratic twists for elliptic curve 4576b1

-4	8	-3	5	-11	13
4576f1	9152m1	41184bg1	114400u1	50336y1	59488w1

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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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