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	598b	Isogeny class
Conductor	598	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-116413856 = -1 · 25 · 13 · 234	Discriminant
Eigenvalues	2+ -3 -3  3 -2 13-  1  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,44,496]	[a1,a2,a3,a4,a6]
Generators	[-5:14:1]	Generators of the group modulo torsion
j	9300746727/116413856	j-invariant
L	0.97237742531546	L(r)(E,1)/r!
Ω	1.380748457056	Real period
R	0.17605984282407	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	4784f1 19136h1 5382m1 14950v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 598b1

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
+	-3	-3	3	-2	-	1	6	-	-6	-4	-7	4	-9	-5	-12	14	0	-2	-3	-10	16	16	2	-14

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Quadratic twists for elliptic curve 598b1

-4	8	-3	5	-7	-11	13	-23
4784f1	19136h1	5382m1	14950v1	29302d1	72358o1	7774e1	13754e1

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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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