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	5472b	Isogeny class
Conductor	5472	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	32832 = 26 · 33 · 19	Discriminant
Eigenvalues	2+ 3+ -2 -4 -6 -4  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-21,36]	[a1,a2,a3,a4,a6]
Generators	[-5:4:1] [0:6:1]	Generators of the group modulo torsion
j	592704/19	j-invariant
L	4.1928469943156	L(r)(E,1)/r!
Ω	3.6715658911543	Real period
R	1.141977869556	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5472p1 10944c1 5472q1 103968bf1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 5472b1

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	-4	0	-	-4	6	-10	-8	-6	-4	-8	10	0	-10	8	-8	-10	-2	-6	-6	-6

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Quadratic twists for elliptic curve 5472b1

-4	8	-3	-19
5472p1	10944c1	5472q1	103968bf1

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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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