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	7728b	Isogeny class
Conductor	7728	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2443906676736 = 211 · 32 · 78 · 23	Discriminant
Eigenvalues	2+ 3+  2 7+  0  6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9632,-352800]	[a1,a2,a3,a4,a6]
j	48260105780546/1193313807	j-invariant
L	1.930551181033	L(r)(E,1)/r!
Ω	0.48263779525824	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3864e4 30912cb3 23184e3 54096u3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7728b3

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	+	0	6	-6	0	-	6	-8	10	-6	8	0	2	-4	10	-8	0	10	16	8	-6	-14

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Quadratic twists for elliptic curve 7728b3

-4	8	-3	-7
3864e4	30912cb3	23184e3	54096u3

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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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