Cremona's table of elliptic curves

12342 = 2 · 3 · 11² · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 17-	Signs for the Atkin-Lehner involutions
Class	12342z	Isogeny class
Conductor	12342	Conductor
∏ cp	168	Product of Tamagawa factors cp
Δ	478773997315080192 = 214 · 36 · 119 · 17	Discriminant
Eigenvalues	2- 3-  0 -2 11+ -4 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1977178178,-33839110688316]	[a1,a2,a3,a4,a6]
j	362515826352179162139875/203046912	j-invariant
L	3.8036222942229	L(r)(E,1)/r!
Ω	0.022640608894184	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	98736bo2 37026d2 12342g2	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 12342z2

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	-2	+	-4	-	0	8	2	8	6	2	-8	-6	2	6	2	0	8	-2	2	4	-2	2

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Quadratic twists for elliptic curve 12342z2

-4	-3	-11
98736bo2	37026d2	12342g2

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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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