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	12138y	Isogeny class
Conductor	12138	Conductor
∏ cp	170	Product of Tamagawa factors cp
deg	24480	Modular degree for the optimal curve
Δ	-451034873856 = -1 · 217 · 35 · 72 · 172	Discriminant
Eigenvalues	2- 3- -3 7+ -5  0 17+  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,1813,12849]	[a1,a2,a3,a4,a6]
Generators	[22:241:1]	Generators of the group modulo torsion
j	2280364702703/1560674304	j-invariant
L	6.4345335528938	L(r)(E,1)/r!
Ω	0.59182308248584	Real period
R	0.063955257052464	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	97104cf1 36414w1 84966dg1 12138u1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138y1

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	+	-5	0	+	6	2	9	3	-6	-6	-4	6	3	-13	-4	8	-6	1	-13	12	-4	-5

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Quadratic twists for elliptic curve 12138y1

-4	-3	-7	17
97104cf1	36414w1	84966dg1	12138u1

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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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