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	342d	Isogeny class
Conductor	342	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	14211126 = 2 · 39 · 192	Discriminant
Eigenvalues	2- 3+  2  0  2 -4  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-299,2053]	[a1,a2,a3,a4,a6]
j	149721291/722	j-invariant
L	2.2375637155543	L(r)(E,1)/r!
Ω	2.2375637155543	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	2736k2 10944g2 342e2 8550a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342d2

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
-	+	2	0	2	-4	0	+	8	-2	-2	-8	-2	4	-4	2	0	-10	0	-16	6	14	-6	-18	10

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Quadratic twists for elliptic curve 342d2

-4	8	-3	5	-7	-11	13	17	-19
2736k2	10944g2	342e2	8550a2	16758t2	41382e2	57798c2	98838z2	6498d2

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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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