Cremona's table of elliptic curves

5112 = 2³ · 3² · 71

Field	Data	Notes
Atkin-Lehner	2+ 3- 71-	Signs for the Atkin-Lehner involutions
Class	5112a	Isogeny class
Conductor	5112	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-86935244544 = -1 · 28 · 314 · 71	Discriminant
Eigenvalues	2+ 3-  2  0  0 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-759,-16310]	[a1,a2,a3,a4,a6]
Generators	[398:7920:1]	Generators of the group modulo torsion
j	-259108432/465831	j-invariant
L	4.2325555995916	L(r)(E,1)/r!
Ω	0.42901275291602	Real period
R	4.9329018436197	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10224a1 40896x1 1704d1 127800bm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5112a1

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

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Quadratic twists for elliptic curve 5112a1

-4	8	-3	5
10224a1	40896x1	1704d1	127800bm1

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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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