Elliptic curve isogeny class with Cremona label 259920dm (LMFDB label 259920.dm)

• Label: 259920dm
• Number of curves: $2$
• Conductor: $259920$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 259920dm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(19\)	\(1\)

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
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 259920dm do not have complex multiplication.

Modular form 259920.2.a.dm

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 259920dm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
259920.dm2	259920dm1	\([0, 0, 0, 3192, 67507]\)	\(44957696/50625\)	\(-4050170910000\)	\([2]\)	\(368640\)	\(1.1056\)	\(\Gamma_0(N)\)-optimal
259920.dm1	259920dm2	\([0, 0, 0, -18183, 636082]\)	\(519388144/164025\)	\(209960859974400\)	\([2]\)	\(737280\)	\(1.4522\)