Elliptic curve isogeny class with LMFDB label 133518.bl (Cremona label 133518ca)

• Label: 133518.bl
• Number of curves: $4$
• Conductor: $133518$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 133518.bl have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(7\)	\(1 + T\)
\(11\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 133518.bl do not have complex multiplication.

Modular form 133518.2.a.bl

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 133518.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
133518.bl1	133518ca4	\([1, 0, 1, -65465, -6449782]\)	\(1285429208617/614922\)	\(14842722204618\)	\([2]\)	\(589824\)	\(1.4823\)
133518.bl2	133518ca3	\([1, 0, 1, -36565, 2643314]\)	\(223980311017/4278582\)	\(103274568247158\)	\([2]\)	\(589824\)	\(1.4823\)
133518.bl3	133518ca2	\([1, 0, 1, -4775, -65194]\)	\(498677257/213444\)	\(5152019277636\)	\([2, 2]\)	\(294912\)	\(1.1357\)
133518.bl4	133518ca1	\([1, 0, 1, 1005, -7394]\)	\(4657463/3696\)	\(-89212455024\)	\([2]\)	\(147456\)	\(0.78912\)	\(\Gamma_0(N)\)-optimal