Cremona's table of elliptic curves

12369 = 3 · 7 · 19 · 31

Field	Data	Notes
Atkin-Lehner	3- 7+ 19- 31+	Signs for the Atkin-Lehner involutions
Class	12369g	Isogeny class
Conductor	12369	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	497071531089 = 34 · 72 · 194 · 312	Discriminant
Eigenvalues	-1 3- -2 7+ -4 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2064,12159]	[a1,a2,a3,a4,a6]
Generators	[-6:159:1]	Generators of the group modulo torsion
j	972447002102017/497071531089	j-invariant
L	2.5439577462072	L(r)(E,1)/r!
Ω	0.82137544938844	Real period
R	3.0971923352485	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	37107j2 86583j2	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 12369g2

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	-	-2	+	-4	-2	2	-	8	-2	+	-2	-6	4	8	-10	4	-2	12	-16	-6	8	12	-6	10

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Quadratic twists for elliptic curve 12369g2

-3	-7
37107j2	86583j2

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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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