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	4576a	Isogeny class
Conductor	4576	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	585728 = 212 · 11 · 13	Discriminant
Eigenvalues	2+  0  2  4 11+ 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-764,-8128]	[a1,a2,a3,a4,a6]
Generators	[221312:5616360:343]	Generators of the group modulo torsion
j	12040481088/143	j-invariant
L	4.400899503301	L(r)(E,1)/r!
Ω	0.90808504720186	Real period
R	9.6927033802875	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	4576d3 9152bd1 41184bf4 114400t4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4576a2

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	2	4	+	+	-6	4	-8	-6	-8	2	6	-4	-8	-2	-12	-14	-12	0	6	0	-4	-6	18

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Quadratic twists for elliptic curve 4576a2

-4	8	-3	5	-11	13
4576d3	9152bd1	41184bf4	114400t4	50336w4	59488t4

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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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