Elliptic curve isogeny class with Cremona label 32400da (LMFDB label 32400.cm)

• Label: 32400da
• Number of curves: $4$
• Conductor: $32400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 32400da have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 32400da do not have complex multiplication.

Modular form 32400.2.a.da

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 32400da

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32400.cm4	32400da1	\([0, 0, 0, 1125, 2250]\)	\(3375/2\)	\(-93312000000\)	\([]\)	\(20736\)	\(0.79428\)	\(\Gamma_0(N)\)-optimal
32400.cm3	32400da2	\([0, 0, 0, -16875, 884250]\)	\(-140625/8\)	\(-30233088000000\)	\([]\)	\(62208\)	\(1.3436\)
32400.cm1	32400da3	\([0, 0, 0, -430875, -108861750]\)	\(-189613868625/128\)	\(-5971968000000\)	\([]\)	\(145152\)	\(1.7672\)
32400.cm2	32400da4	\([0, 0, 0, -340875, -155607750]\)	\(-1159088625/2097152\)	\(-7925422620672000000\)	\([]\)	\(435456\)	\(2.3165\)