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

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

Rank

The elliptic curves in class 138600.dz 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
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 138600.2.a.dz

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.dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
138600.dz1	138600q4	\([0, 0, 0, -831675, -232578250]\)	\(2727138195938/576489375\)	\(13448344140000000000\)	\([2]\)	\(2359296\)	\(2.3850\)
138600.dz2	138600q2	\([0, 0, 0, -264675, 49220750]\)	\(175798419556/12006225\)	\(140040608400000000\)	\([2, 2]\)	\(1179648\)	\(2.0385\)
138600.dz3	138600q1	\([0, 0, 0, -260175, 51079250]\)	\(667932971344/3465\)	\(10103940000000\)	\([2]\)	\(589824\)	\(1.6919\)	\(\Gamma_0(N)\)-optimal
138600.dz4	138600q3	\([0, 0, 0, 230325, 212075750]\)	\(57925453822/866412855\)	\(-20211679081440000000\)	\([2]\)	\(2359296\)	\(2.3850\)