Cremona's table of elliptic curves

47712 = 2⁵ · 3 · 7 · 71

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 71+	Signs for the Atkin-Lehner involutions
Class	47712p	Isogeny class
Conductor	47712	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	-378737856 = -1 · 26 · 35 · 73 · 71	Discriminant
Eigenvalues	2- 3- -3 7- -3  1 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1002,11916]	[a1,a2,a3,a4,a6]
Generators	[-30:126:1] [-4:126:1]	Generators of the group modulo torsion
j	-1740124245952/5917779	j-invariant
L	9.6977435710098	L(r)(E,1)/r!
Ω	1.7003681456433	Real period
R	0.19011066507095	Regulator
r	2	Rank of the group of rational points
S	0.99999999999987	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	47712n1 95424bx1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 47712p1

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
-	-	-3	-	-3	1	-8	0	0	-6	-7	-3	-10	-1	-12	-11	-14	-1	-4	+	-4	-1	9	-3	14

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Quadratic twists for elliptic curve 47712p1

-4	8
47712n1	95424bx1

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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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