Cremona's table of elliptic curves

4715 = 5 · 23 · 41

Field	Data	Notes
Atkin-Lehner	5+ 23+ 41+	Signs for the Atkin-Lehner involutions
Class	4715a	Isogeny class
Conductor	4715	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-58801590125 = -1 · 53 · 234 · 412	Discriminant
Eigenvalues	1  0 5+ -4  6  4  4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,215,11550]	[a1,a2,a3,a4,a6]
Generators	[4078:90007:8]	Generators of the group modulo torsion
j	1096231710231/58801590125	j-invariant
L	3.8156293911848	L(r)(E,1)/r!
Ω	0.84552095270924	Real period
R	4.5127555727137	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	75440q2 42435g2 23575b2 108445g2	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 4715a2

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

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Quadratic twists for elliptic curve 4715a2

-4	-3	5	-23
75440q2	42435g2	23575b2	108445g2

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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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