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	12138b	Isogeny class
Conductor	12138	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2592	Modular degree for the optimal curve
Δ	-764694 = -1 · 2 · 33 · 72 · 172	Discriminant
Eigenvalues	2+ 3+  3 7+ -3 -4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-31,67]	[a1,a2,a3,a4,a6]
Generators	[3:2:1]	Generators of the group modulo torsion
j	-11984473/2646	j-invariant
L	3.1190360890126	L(r)(E,1)/r!
Ω	2.7141362234148	Real period
R	0.57459092548574	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	97104cr1 36414co1 84966cj1 12138p1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138b1

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	+	-3	-4	+	2	-6	3	-5	10	6	-4	-6	9	9	4	8	-6	-11	7	12	0	7

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Quadratic twists for elliptic curve 12138b1

-4	-3	-7	17
97104cr1	36414co1	84966cj1	12138p1

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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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