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	4675m	Isogeny class
Conductor	4675	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	-232216015625 = -1 · 58 · 112 · 173	Discriminant
Eigenvalues	1  3 5-  3 11+  5 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,1133,17666]	[a1,a2,a3,a4,a6]
j	411564375/594473	j-invariant
L	5.375500518794	L(r)(E,1)/r!
Ω	0.67193756484925	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	74800de1 42075cl1 4675i1 51425bk1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4675m1

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	3	-	3	+	5	+	-4	4	0	1	-2	8	-2	6	7	-2	2	2	-13	14	-13	14	-14	10

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Quadratic twists for elliptic curve 4675m1

-4	-3	5	-11	17
74800de1	42075cl1	4675i1	51425bk1	79475bb1

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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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