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	1.3335258025969E+25	Discriminant
Eigenvalues	2- 3-  2 7+ -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-248263722,-1495363594140]	[a1,a2,a3,a4,a6]
Generators	[-9198:104634:1]	Generators of the group modulo torsion
j	70108386184777836280897/552468975892674624	j-invariant
L	8.7524438962465	L(r)(E,1)/r!
Ω	0.038052010781996	Real period
R	4.7919302403351	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	97104cb4 36414t4 84966da4 714g3	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138w3

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 12138w3

-4	-3	-7	17
97104cb4	36414t4	84966da4	714g3

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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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