Cremona's table of elliptic curves

4712 = 2³ · 19 · 31

Field	Data	Notes
Atkin-Lehner	2- 19+ 31+	Signs for the Atkin-Lehner involutions
Class	4712b	Isogeny class
Conductor	4712	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-12972913743872 = -1 · 211 · 193 · 314	Discriminant
Eigenvalues	2- -1  0 -1 -2 -5  7 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3952,-145844]	[a1,a2,a3,a4,a6]
j	3332227702750/6334430539	j-invariant
L	0.74153101217413	L(r)(E,1)/r!
Ω	0.37076550608707	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9424b1 37696d1 42408b1 117800b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4712b1

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	0	-1	-2	-5	7	+	-1	-1	+	-10	0	4	0	3	-5	2	-1	14	-3	14	-6	0	-10

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Quadratic twists for elliptic curve 4712b1

-4	8	-3	5	-19
9424b1	37696d1	42408b1	117800b1	89528d1

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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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