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	12138w	Isogeny class
Conductor	12138	Conductor
∏ cp	768	Product of Tamagawa factors cp
Δ	-5.0670779933169E+27	Discriminant
Eigenvalues	2- 3-  2 7+ -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-84562562,-3437874298932]	[a1,a2,a3,a4,a6]
Generators	[141226:52857136:1]	Generators of the group modulo torsion
j	-2770540998624539614657/209924951154647363208	j-invariant
L	8.7524438962465	L(r)(E,1)/r!
Ω	0.019026005390998	Real period
R	2.3959651201676	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	97104cb5 36414t5 84966da5 714g6	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138w6

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	-2	+	4	-8	-6	0	2	-10	-4	0	6	-4	-6	-12	8	6	0	-12	-6	-2

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Quadratic twists for elliptic curve 12138w6

-4	-3	-7	17
97104cb5	36414t5	84966da5	714g6

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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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