Cremona's table of elliptic curves

342 = 2 · 3² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 19+	Signs for the Atkin-Lehner involutions
Class	342g	Isogeny class
Conductor	342	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-3610152342 = -1 · 2 · 36 · 195	Discriminant
Eigenvalues	2+ 3-  4  3 -2 -1 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-630,6898]	[a1,a2,a3,a4,a6]
j	-37966934881/4952198	j-invariant
L	1.360215538183	L(r)(E,1)/r!
Ω	1.360215538183	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	2736x2 10944bl2 38b2 8550z2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342g2

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
+	-	4	3	-2	-1	-3	+	1	5	-8	-2	8	4	-8	1	-15	2	3	-2	9	-10	6	0	-2

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Quadratic twists for elliptic curve 342g2

-4	8	-3	5	-7	-11	13	17	-19
2736x2	10944bl2	38b2	8550z2	16758o2	41382ct2	57798bu2	98838o2	6498x2

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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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