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	598a	Isogeny class
Conductor	598	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	178802 = 2 · 132 · 232	Discriminant
Eigenvalues	2+  0  0  0 -2 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1802,29898]	[a1,a2,a3,a4,a6]
Generators	[27:6:1]	Generators of the group modulo torsion
j	647326865237625/178802	j-invariant
L	1.5698916376309	L(r)(E,1)/r!
Ω	2.5667675804105	Real period
R	0.6116220454132	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4784e2 19136d2 5382i2 14950t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 598a2

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	0	-2	-	-2	-6	-	-6	8	8	-2	-6	-8	-12	-4	0	10	0	-10	4	-14	14	-14

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Quadratic twists for elliptic curve 598a2

-4	8	-3	5	-7	-11	13	-23
4784e2	19136d2	5382i2	14950t2	29302b2	72358j2	7774c2	13754c2

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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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