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	4675g	Isogeny class
Conductor	4675	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2400	Modular degree for the optimal curve
Δ	-353546875 = -1 · 56 · 113 · 17	Discriminant
Eigenvalues	-2  0 5+  5 11+ -4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,175,156]	[a1,a2,a3,a4,a6]
Generators	[0:12:1]	Generators of the group modulo torsion
j	37933056/22627	j-invariant
L	2.0958166633227	L(r)(E,1)/r!
Ω	1.0407097032911	Real period
R	1.0069170378132	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	74800bs1 42075bo1 187b1 51425w1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4675g1

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
-2	0	+	5	+	-4	+	2	2	-3	4	2	-3	2	-3	-9	-3	-10	-7	2	3	0	-14	1	10

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Quadratic twists for elliptic curve 4675g1

-4	-3	5	-11	17
74800bs1	42075bo1	187b1	51425w1	79475s1

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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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