Elliptic curve isogeny class with Cremona label 468270bd (LMFDB label 468270.bd)

• Label: 468270bd
• Number of curves: $4$
• Conductor: $468270$
• CM: no
• Rank: $0$

Elliptic curves in class 468270bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
468270.bd4	468270bd1	\([1, -1, 0, -2478405, -1500496299]\)	\(35198225176082067/18035507200\)	\(862677031609958400\)	\([2]\)	\(13271040\)	\(2.3931\)	\(\Gamma_0(N)\)-optimal^*
468270.bd2	468270bd2	\([1, -1, 0, -39649605, -96086331819]\)	\(144118734029937784467/37867520\)	\(1811284783165440\)	\([2]\)	\(26542080\)	\(2.7397\)
468270.bd3	468270bd3	\([1, -1, 0, -7589445, 6254314325]\)	\(1386456968640843/318028000000\)	\(11089520331618564000000\)	\([2]\)	\(39813120\)	\(2.9424\)	\(\Gamma_0(N)\)-optimal^*
468270.bd1	468270bd4	\([1, -1, 0, -40259445, -92977543675]\)	\(206956783279200843/12642726098000\)	\(440847246502998583974000\)	\([2]\)	\(79626240\)	\(3.2890\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 468270bd1.

Rank

The elliptic curves in class 468270bd have rank \(0\).

Complex multiplication

The elliptic curves in class 468270bd do not have complex multiplication.

Modular form 468270.2.a.bd

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.