Cremona's table of elliptic curves

7728 = 2⁴ · 3 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 23-	Signs for the Atkin-Lehner involutions
Class	7728s	Isogeny class
Conductor	7728	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	37440	Modular degree for the optimal curve
Δ	-350212539285504 = -1 · 225 · 33 · 75 · 23	Discriminant
Eigenvalues	2- 3-  3 7+ -4  3  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-82104,9072468]	[a1,a2,a3,a4,a6]
j	-14943832855786297/85501108224	j-invariant
L	3.2511480971095	L(r)(E,1)/r!
Ω	0.54185801618492	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	966b1 30912bl1 23184bl1 54096cb1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7728s1

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
-	-	3	+	-4	3	0	0	-	1	2	-5	5	7	3	12	2	-6	12	-10	0	-4	-4	10	19

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Quadratic twists for elliptic curve 7728s1

-4	8	-3	-7
966b1	30912bl1	23184bl1	54096cb1

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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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