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	12138n	Isogeny class
Conductor	12138	Conductor
∏ cp	50	Product of Tamagawa factors cp
Δ	-968649729978548394 = -1 · 2 · 35 · 75 · 179	Discriminant
Eigenvalues	2+ 3-  3 7- -5 -1 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-249847,-67495252]	[a1,a2,a3,a4,a6]
Generators	[2914:153302:1]	Generators of the group modulo torsion
j	-14544652121/8168202	j-invariant
L	4.9587674917654	L(r)(E,1)/r!
Ω	0.10406153124317	Real period
R	0.95304526706953	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	97104bo2 36414cy2 84966bd2 12138d2	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138n2

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	-1	+	0	-4	6	-10	7	0	-9	-2	-9	0	0	-7	-10	-1	-1	-9	15	7

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Quadratic twists for elliptic curve 12138n2

-4	-3	-7	17
97104bo2	36414cy2	84966bd2	12138d2

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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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