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	4598l	Isogeny class
Conductor	4598	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1921964 = 22 · 113 · 192	Discriminant
Eigenvalues	2-  2 -2  4 11+  6  4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-239,1321]	[a1,a2,a3,a4,a6]
j	1134626507/1444	j-invariant
L	5.2464333633016	L(r)(E,1)/r!
Ω	2.6232166816508	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	36784n2 41382j2 114950d2 4598a2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4598l2

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	-2	4	+	6	4	+	8	-6	-10	6	-6	8	0	6	-14	-12	14	6	4	0	0	-14	-2

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Quadratic twists for elliptic curve 4598l2

-4	-3	5	-11	-19
36784n2	41382j2	114950d2	4598a2	87362a2

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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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