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	4576f	Isogeny class
Conductor	4576	Conductor
∏ cp	4	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	[10:22:1]	Generators of the group modulo torsion
j	-649461896/265837	j-invariant
L	4.8693934771631	L(r)(E,1)/r!
Ω	1.7294097695158	Real period
R	0.70390973310599	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	4576b1 9152f1 41184j1 114400g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4576f1

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 4576f1

-4	8	-3	5	-11	13
4576b1	9152f1	41184j1	114400g1	50336l1	59488d1

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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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