Elliptic curve isogeny class with LMFDB label 140400.db (Cremona label 140400bt)

• Label: 140400.db
• Number of curves: $2$
• Conductor: $140400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 140400.db have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 140400.db do not have complex multiplication.

Modular form 140400.2.a.db

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 140400.db

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
140400.db1	140400bt1	\([0, 0, 0, -11340, -464805]\)	\(-20483850240/169\)	\(-1330570800\)	\([]\)	\(124416\)	\(0.92095\)	\(\Gamma_0(N)\)-optimal
140400.db2	140400bt2	\([0, 0, 0, -5940, -907065]\)	\(-327106560/4826809\)	\(-342021893569200\)	\([]\)	\(373248\)	\(1.4703\)