Elliptic curve isogeny class with Cremona label 91260bc (LMFDB label 91260.bc)

• Label: 91260bc
• Number of curves: $2$
• Conductor: $91260$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 91260bc have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 91260bc do not have complex multiplication.

Modular form 91260.2.a.bc

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 91260bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
91260.bc2	91260bc1	\([0, 0, 0, 4563, -59319]\)	\(6912/5\)	\(-7600486523760\)	\([]\)	\(233280\)	\(1.1600\)	\(\Gamma_0(N)\)-optimal
91260.bc1	91260bc2	\([0, 0, 0, -86697, -10024911]\)	\(-5267712/125\)	\(-1710109467846000\)	\([]\)	\(699840\)	\(1.7093\)