Elliptic curve isogeny class with LMFDB label 13520.bc (Cremona label 13520bb)

• Label: 13520.bc
• Number of curves: $4$
• Conductor: $13520$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 13520.bc have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13520.bc do not have complex multiplication.

Modular form 13520.2.a.bc

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 13520.bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13520.bc1	13520bb3	\([0, -1, 0, -6985, 226992]\)	\(488095744/125\)	\(9653618000\)	\([2]\)	\(13824\)	\(0.90183\)
13520.bc2	13520bb4	\([0, -1, 0, -6140, 283100]\)	\(-20720464/15625\)	\(-19307236000000\)	\([2]\)	\(27648\)	\(1.2484\)
13520.bc3	13520bb1	\([0, -1, 0, -225, -820]\)	\(16384/5\)	\(386144720\)	\([2]\)	\(4608\)	\(0.35252\)	\(\Gamma_0(N)\)-optimal
13520.bc4	13520bb2	\([0, -1, 0, 620, -6228]\)	\(21296/25\)	\(-30891577600\)	\([2]\)	\(9216\)	\(0.69910\)