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	4598b	Isogeny class
Conductor	4598	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	7128	Modular degree for the optimal curve
Δ	-8145637478 = -1 · 2 · 118 · 19	Discriminant
Eigenvalues	2+  0  0 -3 11- -1 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-45337,-3704277]	[a1,a2,a3,a4,a6]
j	-48077951625/38	j-invariant
L	0.49076903069626	L(r)(E,1)/r!
Ω	0.16358967689875	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36784y1 41382bt1 114950cc1 4598p1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4598b1

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
+	0	0	-3	-	-1	-5	+	5	-6	2	-3	2	4	-3	2	1	0	3	-4	-15	-10	0	6	2

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Quadratic twists for elliptic curve 4598b1

-4	-3	5	-11	-19
36784y1	41382bt1	114950cc1	4598p1	87362be1

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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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