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	342b	Isogeny class
Conductor	342	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	13463172 = 22 · 311 · 19	Discriminant
Eigenvalues	2- 3-  0  4 -4  0  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-860,9915]	[a1,a2,a3,a4,a6]
j	96386901625/18468	j-invariant
L	2.1705272030281	L(r)(E,1)/r!
Ω	2.1705272030281	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2736o1 10944n1 114b1 8550n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342b1

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	4	-4	0	2	-	2	6	6	-8	-10	-12	-10	-2	-4	-10	0	16	-2	10	16	2	-10

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Quadratic twists for elliptic curve 342b1

-4	8	-3	5	-7	-11	13	17	-19
2736o1	10944n1	114b1	8550n1	16758bb1	41382p1	57798j1	98838bm1	6498k1

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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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