Elliptic curve isogeny class with Cremona label 115920dl (LMFDB label 115920.bh)

• Label: 115920dl
• Number of curves: $2$
• Conductor: $115920$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 115920dl have rank \(2\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 115920.2.a.dl

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 115920dl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
115920.bh2	115920dl1	\([0, 0, 0, -43203, 1455298]\)	\(2986606123201/1421952000\)	\(4245925920768000\)	\([2]\)	\(737280\)	\(1.6927\)	\(\Gamma_0(N)\)-optimal
115920.bh1	115920dl2	\([0, 0, 0, -573123, 166896322]\)	\(6972359126281921/5071500000\)	\(15143417856000000\)	\([2]\)	\(1474560\)	\(2.0393\)