Elliptic curve isogeny class with LMFDB label 115920.dm (Cremona label 115920ck)

• Label: 115920.dm
• Number of curves: $2$
• Conductor: $115920$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 115920.dm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 115920.dm do not have complex multiplication.

Modular form 115920.2.a.dm

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 115920.dm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
115920.dm1	115920ck1	\([0, 0, 0, -183627, -29710854]\)	\(8493409990827/185150000\)	\(14927083315200000\)	\([2]\)	\(737280\)	\(1.8918\)	\(\Gamma_0(N)\)-optimal
115920.dm2	115920ck2	\([0, 0, 0, 15093, -90638406]\)	\(4716275733/44023437500\)	\(-3549238560000000000\)	\([2]\)	\(1474560\)	\(2.2383\)