Cremona's table of elliptic curves

5472 = 2⁵ · 3² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 19+	Signs for the Atkin-Lehner involutions
Class	5472g	Isogeny class
Conductor	5472	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1792	Modular degree for the optimal curve
Δ	-50528448 = -1 · 26 · 37 · 192	Discriminant
Eigenvalues	2+ 3- -2 -4 -6 -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-21,344]	[a1,a2,a3,a4,a6]
Generators	[-5:18:1] [1:18:1]	Generators of the group modulo torsion
j	-21952/1083	j-invariant
L	4.1953192489967	L(r)(E,1)/r!
Ω	1.6604145060257	Real period
R	0.63166745920525	Regulator
r	2	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5472m1 10944cm2 1824f1 103968ci1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 5472g1

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	-6	-2	-6	+	6	-4	0	-6	-12	0	-2	-12	-8	2	-4	-12	-10	16	6	4	14

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Quadratic twists for elliptic curve 5472g1

-4	8	-3	-19
5472m1	10944cm2	1824f1	103968ci1

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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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