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	8	Product of Tamagawa factors cp
deg	108800	Modular degree for the optimal curve
Δ	-7650341088574464 = -1 · 210 · 32 · 7 · 179	Discriminant
Eigenvalues	2+ 3+  2 7+  0  4 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-156499,24133165]	[a1,a2,a3,a4,a6]
Generators	[342:3109:1]	Generators of the group modulo torsion
j	-3574558889/64512	j-invariant
L	3.3195517600218	L(r)(E,1)/r!
Ω	0.41732660808112	Real period
R	3.9771628452895	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	97104cp1 36414ci1 84966by1 12138l1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138a1

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 12138a1

-4	-3	-7	17
97104cp1	36414ci1	84966by1	12138l1

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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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