Cremona's table of elliptic curves

4598 = 2 · 11² · 19

Field	Data	Notes
Atkin-Lehner	2- 11- 19+	Signs for the Atkin-Lehner involutions
Class	4598o	Isogeny class
Conductor	4598	Conductor
∏ cp	19	Product of Tamagawa factors cp
deg	1824	Modular degree for the optimal curve
Δ	-1205338112 = -1 · 219 · 112 · 19	Discriminant
Eigenvalues	2- -1  2 -3 11-  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-272,2289]	[a1,a2,a3,a4,a6]
Generators	[-11:69:1]	Generators of the group modulo torsion
j	-18396908233/9961472	j-invariant
L	4.7737687394328	L(r)(E,1)/r!
Ω	1.4289200983499	Real period
R	0.17583277509784	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	36784be1 41382u1 114950j1 4598j1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4598o1

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	2	-3	-	2	2	+	-1	-5	-8	3	6	-2	-3	1	-3	6	-12	-14	-6	4	2	-4	-4

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Quadratic twists for elliptic curve 4598o1

-4	-3	5	-11	-19
36784be1	41382u1	114950j1	4598j1	87362o1

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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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