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	7728j	Isogeny class
Conductor	7728	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-102562553856 = -1 · 213 · 3 · 73 · 233	Discriminant
Eigenvalues	2- 3+ -3 7+  0  5  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-432,15936]	[a1,a2,a3,a4,a6]
Generators	[32:-184:1]	Generators of the group modulo torsion
j	-2181825073/25039686	j-invariant
L	2.6834476233352	L(r)(E,1)/r!
Ω	0.90279889279001	Real period
R	0.2476970641677	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	966k2 30912cd2 23184bk2 54096di2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7728j2

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	+	0	5	0	-8	-	3	-2	-7	9	1	3	-12	6	14	4	-6	-4	16	12	6	-1

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Quadratic twists for elliptic curve 7728j2

-4	8	-3	-7
966k2	30912cd2	23184bk2	54096di2

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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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