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

• Label: 468270.bf
• Number of curves: $4$
• Conductor: $468270$
• CM: no
• Rank: $1$

Elliptic curves in class 468270.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
468270.bf1	468270bf3	\([1, -1, 0, -913149, 333800055]\)	\(65202655558249/512820150\)	\(662290797582775350\)	\([2]\)	\(8847360\)	\(2.2477\)	\(\Gamma_0(N)\)-optimal^*
468270.bf2	468270bf2	\([1, -1, 0, -96399, -2864295]\)	\(76711450249/41602500\)	\(53728296180322500\)	\([2, 2]\)	\(4423680\)	\(1.9012\)	\(\Gamma_0(N)\)-optimal^*
468270.bf3	468270bf1	\([1, -1, 0, -74619, -7817067]\)	\(35578826569/51600\)	\(66639747200400\)	\([2]\)	\(2211840\)	\(1.5546\)	\(\Gamma_0(N)\)-optimal^*
468270.bf4	468270bf4	\([1, -1, 0, 371871, -22812597]\)	\(4403686064471/2721093750\)	\(-3514205418771093750\)	\([2]\)	\(8847360\)	\(2.2477\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 468270.bf1.

Rank

The elliptic curves in class 468270.bf have rank \(1\).

Complex multiplication

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

Modular form 468270.2.a.bf

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.