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	8	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	23934528 = 26 · 39 · 19	Discriminant
Eigenvalues	2+ 3-  0 -4  0 -4 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-72,0]	[a1,a2,a3,a4,a6]
Generators	[-3:15:1]	Generators of the group modulo torsion
j	57066625/32832	j-invariant
L	1.2648109167857	L(r)(E,1)/r!
Ω	1.7816724979966	Real period
R	0.35495045195117	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2736n1 10944o1 114a1 8550bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342c1

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 342c1

-4	8	-3	5	-7	-11	13	17	-19
2736n1	10944o1	114a1	8550bf1	16758g1	41382bu1	57798bf1	98838q1	6498v1

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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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