Cremona's table of elliptic curves

598 = 2 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 13+ 23+	Signs for the Atkin-Lehner involutions
Class	598c	Isogeny class
Conductor	598	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-13754 = -1 · 2 · 13 · 232	Discriminant
Eigenvalues	2- -1  3  3  2 13+ -1 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-14,-27]	[a1,a2,a3,a4,a6]
j	-304821217/13754	j-invariant
L	2.4607219644981	L(r)(E,1)/r!
Ω	1.230360982249	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	4784d1 19136k1 5382e1 14950j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 598c1

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	3	3	2	+	-1	-4	+	0	8	3	-2	-1	-3	-2	0	-4	-10	3	-12	8	6	-14	-12

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Quadratic twists for elliptic curve 598c1

-4	8	-3	5	-7	-11	13	-23
4784d1	19136k1	5382e1	14950j1	29302h1	72358e1	7774a1	13754g1

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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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