Elliptic curve isogeny class with Cremona label 137280gz (LMFDB label 137280.m)

• Label: 137280gz
• Number of curves: $2$
• Conductor: $137280$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 137280gz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(11\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 137280gz do not have complex multiplication.

Modular form 137280.2.a.gz

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 137280gz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
137280.m2	137280gz1	\([0, -1, 0, -42721, 4578145]\)	\(-32894113444921/15289560000\)	\(-4008066416640000\)	\([2]\)	\(737280\)	\(1.7001\)	\(\Gamma_0(N)\)-optimal
137280.m1	137280gz2	\([0, -1, 0, -746721, 248584545]\)	\(175654575624148921/21954418200\)	\(5755219004620800\)	\([2]\)	\(1474560\)	\(2.0467\)