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	598d	Isogeny class
Conductor	598	Conductor
∏ cp	34	Product of Tamagawa factors cp
deg	272	Modular degree for the optimal curve
Δ	-901382144 = -1 · 217 · 13 · 232	Discriminant
Eigenvalues	2- -1 -1 -1 -6 13+  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,4,-1443]	[a1,a2,a3,a4,a6]
Generators	[21:81:1]	Generators of the group modulo torsion
j	6967871/901382144	j-invariant
L	2.3415704003666	L(r)(E,1)/r!
Ω	0.72465340410426	Real period
R	0.095038148262024	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	4784c1 19136o1 5382c1 14950f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 598d1

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	-1	-1	-6	+	3	-4	-	0	-8	7	-2	11	-11	-10	0	12	-2	-13	4	8	14	10	4

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Quadratic twists for elliptic curve 598d1

-4	8	-3	5	-7	-11	13	-23
4784c1	19136o1	5382c1	14950f1	29302i1	72358f1	7774b1	13754f1

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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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