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	7728p	Isogeny class
Conductor	7728	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	101376	Modular degree for the optimal curve
Δ	-417391501715177472 = -1 · 234 · 38 · 7 · 232	Discriminant
Eigenvalues	2- 3-  2 7+  4 -4 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-235912,-54035212]	[a1,a2,a3,a4,a6]
Generators	[1724:68310:1]	Generators of the group modulo torsion
j	-354499561600764553/101902222098432	j-invariant
L	5.6149948677272	L(r)(E,1)/r!
Ω	0.10672624536817	Real period
R	3.2881994304432	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	966c1 30912bi1 23184br1 54096bo1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7728p1

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	2	+	-6	-6	-2	-10	-8	-10	-6	12	-10	-8	4	-2	8	6	0	-8

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Quadratic twists for elliptic curve 7728p1

-4	8	-3	-7
966c1	30912bi1	23184br1	54096bo1

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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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