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	8	Product of Tamagawa factors cp
Δ	-31079732562 = -1 · 2 · 316 · 192	Discriminant
Eigenvalues	2- 3-  0  4 -4  0  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-770,12003]	[a1,a2,a3,a4,a6]
j	-69173457625/42633378	j-invariant
L	2.1705272030281	L(r)(E,1)/r!
Ω	1.085263601514	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	2736o2 10944n2 114b2 8550n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342b2

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 342b2

-4	8	-3	5	-7	-11	13	17	-19
2736o2	10944n2	114b2	8550n2	16758bb2	41382p2	57798j2	98838bm2	6498k2

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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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