Elliptic curve isogeny class with LMFDB label 138600.bq (Cremona label 138600dz)

• Label: 138600.bq
• Number of curves: $4$
• Conductor: $138600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 138600.bq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 138600.bq do not have complex multiplication.

Modular form 138600.2.a.bq

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 138600.bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
138600.bq1	138600dz3	\([0, 0, 0, -6654675, 6607516750]\)	\(1397097631688978/433125\)	\(10103940000000000\)	\([2]\)	\(3145728\)	\(2.4335\)
138600.bq2	138600dz2	\([0, 0, 0, -417675, 102325750]\)	\(690862540036/12006225\)	\(140040608400000000\)	\([2, 2]\)	\(1572864\)	\(2.0869\)
138600.bq3	138600dz1	\([0, 0, 0, -53175, -2285750]\)	\(5702413264/2525985\)	\(7365772260000000\)	\([2]\)	\(786432\)	\(1.7403\)	\(\Gamma_0(N)\)-optimal
138600.bq4	138600dz4	\([0, 0, 0, -12675, 292270750]\)	\(-9653618/1581886845\)	\(-36902256320160000000\)	\([2]\)	\(3145728\)	\(2.4335\)