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	7728g	Isogeny class
Conductor	7728	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	800	Modular degree for the optimal curve
Δ	-1978368 = -1 · 212 · 3 · 7 · 23	Discriminant
Eigenvalues	2- 3+  0 7+ -1  2  4  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,27,-51]	[a1,a2,a3,a4,a6]
j	512000/483	j-invariant
L	1.4340667301071	L(r)(E,1)/r!
Ω	1.4340667301071	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	483b1 30912bu1 23184bm1 54096ck1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7728g1

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	+	-1	2	4	3	+	-6	2	-2	1	8	5	3	-5	13	0	0	-16	2	-6	6	10

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Quadratic twists for elliptic curve 7728g1

-4	8	-3	-7
483b1	30912bu1	23184bm1	54096ck1

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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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