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	342a	Isogeny class
Conductor	342	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	60	Modular degree for the optimal curve
Δ	-110808 = -1 · 23 · 36 · 19	Discriminant
Eigenvalues	2- 3-  0 -1  6  5 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-140,-601]	[a1,a2,a3,a4,a6]
j	-413493625/152	j-invariant
L	2.0830123793835	L(r)(E,1)/r!
Ω	0.69433745979451	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	2736m1 10944l1 38a3 8550i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342a1

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	-1	6	5	-3	-	-3	-9	-4	2	0	8	0	3	-9	-10	5	6	-7	-10	6	12	-10

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Quadratic twists for elliptic curve 342a1

-4	8	-3	5	-7	-11	13	17	-19
2736m1	10944l1	38a3	8550i1	16758bc1	41382m1	57798h1	98838bl1	6498j1

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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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