Cremona's table of elliptic curves

2728 = 2³ · 11 · 31

Field	Data	Notes
Atkin-Lehner	2+ 11+ 31+	Signs for the Atkin-Lehner involutions
Class	2728b	Isogeny class
Conductor	2728	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7200	Modular degree for the optimal curve
Δ	-55426036336 = -1 · 24 · 112 · 315	Discriminant
Eigenvalues	2+  2 -3  3 11+  0 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-48972,-4155019]	[a1,a2,a3,a4,a6]
Generators	[2266:17193:8]	Generators of the group modulo torsion
j	-811813221498166528/3464127271	j-invariant
L	3.9828618532611	L(r)(E,1)/r!
Ω	0.16046552767994	Real period
R	6.2051674132859	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	5456e1 21824i1 24552u1 68200s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2728b1

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	-3	3	+	0	-6	-1	-4	-8	+	4	9	-4	-8	2	-1	4	0	3	-14	12	-12	0	13

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Quadratic twists for elliptic curve 2728b1

-4	8	-3	5	-11	-31
5456e1	21824i1	24552u1	68200s1	30008f1	84568g1

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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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