Elliptic curve isogeny class with LMFDB label 91091.o (Cremona label 91091j)

• Label: 91091.o
• Number of curves: $2$
• Conductor: $91091$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 91091.o have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 91091.o do not have complex multiplication.

Modular form 91091.2.a.o

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 91091.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
91091.o1	91091j1	\([1, 1, 0, -809, -6040]\)	\(226981/77\)	\(19902563681\)	\([2]\)	\(62208\)	\(0.67838\)	\(\Gamma_0(N)\)-optimal
91091.o2	91091j2	\([1, 1, 0, 2376, -38527]\)	\(5735339/5929\)	\(-1532497403437\)	\([2]\)	\(124416\)	\(1.0250\)