Elliptic curve isogeny class with Cremona label 32448di (LMFDB label 32448.dg)

• Label: 32448di
• Number of curves: $4$
• Conductor: $32448$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 32448di have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 32448di do not have complex multiplication.

Modular form 32448.2.a.di

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 32448di

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32448.dg4	32448di1	\([0, 1, 0, 3103, 28575]\)	\(5735339/3888\)	\(-2239217270784\)	\([2]\)	\(46080\)	\(1.0584\)	\(\Gamma_0(N)\)-optimal
32448.dg3	32448di2	\([0, 1, 0, -13537, 224927]\)	\(476379541/236196\)	\(136032449200128\)	\([2]\)	\(92160\)	\(1.4050\)
32448.dg2	32448di3	\([0, 1, 0, -283937, -58365345]\)	\(-4395631034341/3145728\)	\(-1811720284667904\)	\([2]\)	\(230400\)	\(1.8632\)
32448.dg1	32448di4	\([0, 1, 0, -4543777, -3729495457]\)	\(18013780041269221/9216\)	\(5307774271488\)	\([2]\)	\(460800\)	\(2.2097\)