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	12138k	Isogeny class
Conductor	12138	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	-5583888662184 = -1 · 23 · 35 · 7 · 177	Discriminant
Eigenvalues	2+ 3- -1 7- -3 -3 17+  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-10844,-450142]	[a1,a2,a3,a4,a6]
Generators	[126:370:1]	Generators of the group modulo torsion
j	-5841725401/231336	j-invariant
L	3.7752857074106	L(r)(E,1)/r!
Ω	0.23338342718222	Real period
R	0.80881615138486	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	97104bg1 36414cr1 84966l1 714b1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138k1

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
+	-	-1	-	-3	-3	+	6	2	-6	-4	11	-12	3	12	5	4	6	9	-12	-15	11	7	-13	-11

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Quadratic twists for elliptic curve 12138k1

-4	-3	-7	17
97104bg1	36414cr1	84966l1	714b1

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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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