Elliptic curve isogeny class with LMFDB label 158400.p (Cremona label 158400gb)

• Label: 158400.p
• Number of curves: $2$
• Conductor: $158400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 158400.p have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 158400.p do not have complex multiplication.

Modular form 158400.2.a.p

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.

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

Isogeny graph

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

Elliptic curves in class 158400.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
158400.p1	158400gb2	\([0, 0, 0, -4063500, -2928150000]\)	\(736314327/58564\)	\(590190188544000000000\)	\([2]\)	\(7372800\)	\(2.7291\)
158400.p2	158400gb1	\([0, 0, 0, 256500, -206550000]\)	\(185193/1936\)	\(-19510419456000000000\)	\([2]\)	\(3686400\)	\(2.3825\)	\(\Gamma_0(N)\)-optimal