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	12138l	Isogeny class
Conductor	12138	Conductor
∏ cp	200	Product of Tamagawa factors cp
Δ	-19503362943036 = -1 · 22 · 310 · 75 · 173	Discriminant
Eigenvalues	2+ 3- -2 7-  0  4 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,3198,-200480]	[a1,a2,a3,a4,a6]
Generators	[59:411:1]	Generators of the group modulo torsion
j	736558976791/3969746172	j-invariant
L	3.9134975162825	L(r)(E,1)/r!
Ω	0.34413633709984	Real period
R	0.22743878482947	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	97104bk3 36414cs3 84966s3 12138a3	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138l3

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	4	+	0	6	-4	0	2	-10	-4	-12	6	-10	-10	-12	-10	14	4	6	0	2

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Quadratic twists for elliptic curve 12138l3

-4	-3	-7	17
97104bk3	36414cs3	84966s3	12138a3

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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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