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	342c	Isogeny class
Conductor	342	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-617336050482 = -1 · 2 · 38 · 196	Discriminant
Eigenvalues	2+ 3-  0 -4  0 -4 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3762,97470]	[a1,a2,a3,a4,a6]
Generators	[39:75:1]	Generators of the group modulo torsion
j	-8078253774625/846825858	j-invariant
L	1.2648109167857	L(r)(E,1)/r!
Ω	0.89083624899831	Real period
R	2.129702711707	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	2736n4 10944o4 114a4 8550bf4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342c4

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	0	-4	-6	-	6	-6	2	-4	-6	-4	-6	-6	12	14	8	0	14	-10	12	6	-10

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Quadratic twists for elliptic curve 342c4

-4	8	-3	5	-7	-11	13	17	-19
2736n4	10944o4	114a4	8550bf4	16758g4	41382bu4	57798bf4	98838q4	6498v4

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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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