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	12138ba	Isogeny class
Conductor	12138	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	150764993878968 = 23 · 38 · 7 · 177	Discriminant
Eigenvalues	2- 3-  2 7-  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1467837,684363897]	[a1,a2,a3,a4,a6]
j	14489843500598257/6246072	j-invariant
L	5.6490592167868	L(r)(E,1)/r!
Ω	0.47075493473223	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	97104bi4 36414bh4 84966cw4 714f4	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138ba4

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	-	0	-6	+	0	8	6	8	-10	6	12	0	-10	-8	-6	12	0	6	8	16	2	-2

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Quadratic twists for elliptic curve 12138ba4

-4	-3	-7	17
97104bi4	36414bh4	84966cw4	714f4

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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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