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	7728a	Isogeny class
Conductor	7728	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	15143417856 = 211 · 38 · 72 · 23	Discriminant
Eigenvalues	2+ 3+  2 7+ -4  4  4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-792,6480]	[a1,a2,a3,a4,a6]
Generators	[2:70:1]	Generators of the group modulo torsion
j	26860713266/7394247	j-invariant
L	3.9061417164809	L(r)(E,1)/r!
Ω	1.1611502935528	Real period
R	1.6820138349744	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	3864d2 30912bx2 23184k2 54096r2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7728a2

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

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Quadratic twists for elliptic curve 7728a2

-4	8	-3	-7
3864d2	30912bx2	23184k2	54096r2

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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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