Cremona's table of elliptic curves

4675 = 5² · 11 · 17

Field	Data	Notes
Atkin-Lehner	5+ 11+ 17-	Signs for the Atkin-Lehner involutions
Class	4675h	Isogeny class
Conductor	4675	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-4525233205423046875 = -1 · 58 · 119 · 173	Discriminant
Eigenvalues	0  2 5+ -5 11+  4 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-241383,112146043]	[a1,a2,a3,a4,a6]
j	-99546392709922816/289614925147075	j-invariant
L	1.2935251048123	L(r)(E,1)/r!
Ω	0.21558751746872	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	74800cm2 42075bf2 935b2 51425g2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4675h2

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
0	2	+	-5	+	4	-	-4	-6	-3	2	-8	9	4	3	9	9	14	-5	6	-11	8	-6	9	4

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Quadratic twists for elliptic curve 4675h2

-4	-3	5	-11	17
74800cm2	42075bf2	935b2	51425g2	79475i2

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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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