Elliptic curve isogeny class with Cremona label 67518bo (LMFDB label 67518.bx)

• Label: 67518bo
• Number of curves: $4$
• Conductor: $67518$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 67518bo have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(11\)	\(1\)
\(31\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 67518bo do not have complex multiplication.

Modular form 67518.2.a.bo

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 67518bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
67518.bx4	67518bo1	\([1, -1, 1, -749, 39493]\)	\(-35937/496\)	\(-640568112624\)	\([2]\)	\(92160\)	\(0.94703\)	\(\Gamma_0(N)\)-optimal
67518.bx3	67518bo2	\([1, -1, 1, -22529, 1302733]\)	\(979146657/3844\)	\(4964402872836\)	\([2, 2]\)	\(184320\)	\(1.2936\)
67518.bx2	67518bo3	\([1, -1, 1, -33419, -78119]\)	\(3196010817/1847042\)	\(2385395580397698\)	\([2]\)	\(368640\)	\(1.6402\)
67518.bx1	67518bo4	\([1, -1, 1, -360119, 83269585]\)	\(3999236143617/62\)	\(80071014078\)	\([2]\)	\(368640\)	\(1.6402\)