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	5112b	Isogeny class
Conductor	5112	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	101603331072 = 210 · 39 · 712	Discriminant
Eigenvalues	2- 3- -2  2  4  2 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4971,-134026]	[a1,a2,a3,a4,a6]
Generators	[187:2340:1]	Generators of the group modulo torsion
j	18198161572/136107	j-invariant
L	3.7423441309279	L(r)(E,1)/r!
Ω	0.56883254067348	Real period
R	3.2894954695252	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	10224d2 40896n2 1704b2 127800g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5112b2

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

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Quadratic twists for elliptic curve 5112b2

-4	8	-3	5
10224d2	40896n2	1704b2	127800g2

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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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