Cremona's table of elliptic curves

1472 = 2⁶ · 23

Field	Data	Notes
Atkin-Lehner	2+ 23+	Signs for the Atkin-Lehner involutions
Class	1472a	Isogeny class
Conductor	1472	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-23552 = -1 · 210 · 23	Discriminant
Eigenvalues	2+  1  2 -4  2 -7 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-17,23]	[a1,a2,a3,a4,a6]
Generators	[2:1:1]	Generators of the group modulo torsion
j	-562432/23	j-invariant
L	3.1362245999141	L(r)(E,1)/r!
Ω	3.7648642992272	Real period
R	0.83302460610808	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	1472n1 184b1 13248x1 36800x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1472a1

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
+	1	2	-4	2	-7	-4	6	+	-5	3	-2	-9	-8	-1	6	8	10	-2	-13	-3	6	0	-4	-8

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Quadratic twists for elliptic curve 1472a1

-4	8	-3	5	-7	-23
1472n1	184b1	13248x1	36800x1	72128e1	33856i1

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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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