Elliptic curve isogeny class with Cremona label 91200gw (LMFDB label 91200.be)

• Label: 91200gw
• Number of curves: $2$
• Conductor: $91200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 91200gw have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 91200gw do not have complex multiplication.

Modular form 91200.2.a.gw

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 91200gw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
91200.be1	91200gw1	\([0, -1, 0, -1272033, 552715137]\)	\(-1389310279182025/267418692\)	\(-43813878497280000\)	\([]\)	\(1382400\)	\(2.1937\)	\(\Gamma_0(N)\)-optimal
91200.be2	91200gw2	\([0, -1, 0, 7635167, -486022463]\)	\(480705753733655/279172334592\)	\(-28587247062220800000000\)	\([]\)	\(6912000\)	\(2.9984\)