Cremona's table of elliptic curves

2023 = 7 · 17²

Field	Data	Notes
Atkin-Lehner	7- 17+	Signs for the Atkin-Lehner involutions
Class	2023b	Isogeny class
Conductor	2023	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	99127 = 73 · 172	Discriminant
Eigenvalues	-1 -3 -4 7-  0 -2 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-12,0]	[a1,a2,a3,a4,a6]
Generators	[-3:2:1] [-2:4:1]	Generators of the group modulo torsion
j	610929/343	j-invariant
L	1.4526302190012	L(r)(E,1)/r!
Ω	2.7768814163883	Real period
R	0.17437189436434	Regulator
r	2	Rank of the group of rational points
S	0.99999999999926	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32368l1 129472bi1 18207f1 50575b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2023b1

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

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Quadratic twists for elliptic curve 2023b1

-4	8	-3	5	-7	17
32368l1	129472bi1	18207f1	50575b1	14161c1	2023a1

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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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