Elliptic curve isogeny class with Cremona label 125840bn (LMFDB label 125840.cl)

• Label: 125840bn
• Number of curves: $4$
• Conductor: $125840$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 125840bn have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 125840bn do not have complex multiplication.

Modular form 125840.2.a.bn

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 125840bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
125840.cl4	125840bn1	\([0, -1, 0, 201304, -805264]\)	\(124326214271/71980480\)	\(-522312954385530880\)	\([2]\)	\(2211840\)	\(2.0892\)	\(\Gamma_0(N)\)-optimal
125840.cl3	125840bn2	\([0, -1, 0, -805416, -5637520]\)	\(7962857630209/4606058600\)	\(33423006840727961600\)	\([2]\)	\(4423680\)	\(2.4358\)
125840.cl2	125840bn3	\([0, -1, 0, -2780136, -1904156560]\)	\(-327495950129089/26547449500\)	\(-192636625648310272000\)	\([2]\)	\(6635520\)	\(2.6385\)
125840.cl1	125840bn4	\([0, -1, 0, -45314056, -117392256144]\)	\(1418098748958579169/8307406250\)	\(60281147079296000000\)	\([2]\)	\(13271040\)	\(2.9851\)