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
deg	60	Modular degree for the optimal curve
Δ	-443232 = -1 · 25 · 36 · 19	Discriminant
Eigenvalues	2+ 3-  4  3 -2 -1 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,0,-32]	[a1,a2,a3,a4,a6]
j	-1/608	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	2736x1 10944bl1 38b1 8550z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342g1

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 342g1

-4	8	-3	5	-7	-11	13	17	-19
2736x1	10944bl1	38b1	8550z1	16758o1	41382ct1	57798bu1	98838o1	6498x1

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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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