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	12138x	Isogeny class
Conductor	12138	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-17234224266 = -1 · 2 · 3 · 7 · 177	Discriminant
Eigenvalues	2- 3- -3 7+  1  3 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,283,-6021]	[a1,a2,a3,a4,a6]
Generators	[1332:5403:64]	Generators of the group modulo torsion
j	103823/714	j-invariant
L	6.8511452050568	L(r)(E,1)/r!
Ω	0.61388838124748	Real period
R	2.7900614404587	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	97104ce1 36414v1 84966db1 714h1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138x1

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	+	1	3	+	-6	2	-6	0	-3	0	11	0	-9	-4	14	-7	-12	1	5	3	-1	13

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Quadratic twists for elliptic curve 12138x1

-4	-3	-7	17
97104ce1	36414v1	84966db1	714h1

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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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