Elliptic curve isogeny class with Cremona label 162450ba (LMFDB label 162450.dk)

• Label: 162450ba
• Number of curves: $2$
• Conductor: $162450$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 162450ba have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 162450ba do not have complex multiplication.

Modular form 162450.2.a.ba

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 162450ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162450.dk2	162450ba1	\([1, -1, 1, 15504160, 1395133827]\)	\(480705753733655/279172334592\)	\(-239365481167867648435200\)	\([]\)	\(20736000\)	\(3.1755\)	\(\Gamma_0(N)\)-optimal
162450.dk1	162450ba2	\([1, -1, 1, -1614389180, -24970409509053]\)	\(-1389310279182025/267418692\)	\(-89565537730220491289062500\)	\([]\)	\(103680000\)	\(3.9802\)