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
Δ	-1534801608 = -1 · 23 · 312 · 192	Discriminant
Eigenvalues	2+ 3-  0 -4  0 -4 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,288,-216]	[a1,a2,a3,a4,a6]
Generators	[15:78:1]	Generators of the group modulo torsion
j	3616805375/2105352	j-invariant
L	1.2648109167857	L(r)(E,1)/r!
Ω	0.89083624899831	Real period
R	0.70990090390234	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	2736n2 10944o2 114a2 8550bf2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342c2

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 342c2

-4	8	-3	5	-7	-11	13	17	-19
2736n2	10944o2	114a2	8550bf2	16758g2	41382bu2	57798bf2	98838q2	6498v2

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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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