Cremona's table of elliptic curves

12138 = 2 · 3 · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	12138bb	Isogeny class
Conductor	12138	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	22542021669220578 = 2 · 34 · 78 · 176	Discriminant
Eigenvalues	2- 3-  2 7-  4  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-264152,-51775458]	[a1,a2,a3,a4,a6]
j	84448510979617/933897762	j-invariant
L	6.7433585710794	L(r)(E,1)/r!
Ω	0.21072995534623	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	97104bj6 36414bi6 84966cz6 42a5	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138bb5

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

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Quadratic twists for elliptic curve 12138bb5

-4	-3	-7	17
97104bj6	36414bi6	84966cz6	42a5

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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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