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	4598i	Isogeny class
Conductor	4598	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	3168	Modular degree for the optimal curve
Δ	-8145637478 = -1 · 2 · 118 · 19	Discriminant
Eigenvalues	2+  1  0 -1 11-  2  6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-971,12340]	[a1,a2,a3,a4,a6]
Generators	[-182:38809:343]	Generators of the group modulo torsion
j	-471625/38	j-invariant
L	3.1530950869483	L(r)(E,1)/r!
Ω	1.2850926459531	Real period
R	7.3607807893334	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	36784v1 41382ce1 114950cw1 4598m1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4598i1

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	0	-1	-	2	6	-	-9	3	8	-7	0	-10	9	-9	-9	8	-4	12	2	14	-12	6	-16

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Quadratic twists for elliptic curve 4598i1

-4	-3	5	-11	-19
36784v1	41382ce1	114950cw1	4598m1	87362bn1

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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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