Elliptic curve isogeny class with Cremona label 273600jj (LMFDB label 273600.jj)

• Label: 273600jj
• Number of curves: $2$
• Conductor: $273600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 273600jj have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 273600jj do not have complex multiplication.

Modular form 273600.2.a.jj

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 273600jj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
273600.jj2	273600jj1	\([0, 0, 0, 2368500, 871850000]\)	\(3936827539/3158028\)	\(-1178727634944000000000\)	\([2]\)	\(10321920\)	\(2.7311\)	\(\Gamma_0(N)\)-optimal
273600.jj1	273600jj2	\([0, 0, 0, -11311500, 7575050000]\)	\(428831641421/181752822\)	\(67838877305856000000000\)	\([2]\)	\(20643840\)	\(3.0777\)