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	12138a	Isogeny class
Conductor	12138	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	557837371041888 = 25 · 3 · 72 · 179	Discriminant
Eigenvalues	2+ 3+  2 7+  0  4 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2514739,1533878413]	[a1,a2,a3,a4,a6]
Generators	[116445:49628:125]	Generators of the group modulo torsion
j	14830727012009/4704	j-invariant
L	3.3195517600218	L(r)(E,1)/r!
Ω	0.41732660808112	Real period
R	7.954325690579	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	97104cp2 36414ci2 84966by2 12138l2	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138a2

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 12138a2

-4	-3	-7	17
97104cp2	36414ci2	84966by2	12138l2

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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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