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	12138u	Isogeny class
Conductor	12138	Conductor
∏ cp	34	Product of Tamagawa factors cp
deg	416160	Modular degree for the optimal curve
Δ	-1.0886885389105E+19	Discriminant
Eigenvalues	2- 3+  3 7-  5  0 17-  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,523951,62603183]	[a1,a2,a3,a4,a6]
j	2280364702703/1560674304	j-invariant
L	4.8802981615355	L(r)(E,1)/r!
Ω	0.14353818122163	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	97104cn1 36414bo1 84966ee1 12138y1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138u1

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
-	+	3	-	5	0	-	6	-2	-9	-3	6	6	-4	6	3	-13	4	8	6	-1	13	12	-4	5

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Quadratic twists for elliptic curve 12138u1

-4	-3	-7	17
97104cn1	36414bo1	84966ee1	12138y1

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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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