Elliptic curve isogeny class with Cremona label 243360ff (LMFDB label 243360.ff)

• Label: 243360ff
• Number of curves: $4$
• Conductor: $243360$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 243360ff have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 243360ff do not have complex multiplication.

Modular form 243360.2.a.ff

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 243360ff

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
243360.ff3	243360ff1	\([0, 0, 0, -24747177, -26813576504]\)	\(7442744143086784/2927948765625\)	\(659372892900519681000000\)	\([2, 2]\)	\(33030144\)	\(3.2690\)	\(\Gamma_0(N)\)-optimal
243360.ff2	243360ff2	\([0, 0, 0, -178748427, 900920753746]\)	\(350584567631475848/8259273550125\)	\(14879880844746068234304000\)	\([2]\)	\(66060288\)	\(3.6156\)
243360.ff4	243360ff3	\([0, 0, 0, 79357668, -193547896256]\)	\(3834800837445824/3342041015625\)	\(-48168083344329000000000000\)	\([2]\)	\(66060288\)	\(3.6156\)
243360.ff1	243360ff4	\([0, 0, 0, -346058427, -2477068906754]\)	\(2543984126301795848/909361981125\)	\(1638303640357987077696000\)	\([2]\)	\(66060288\)	\(3.6156\)