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

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

Elliptic curves in class 468270bf

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
468270.bf3	468270bf1	[1, -1, 0, -74619, -7817067]	[2]	2211840	\(\Gamma_0(N)\)-optimal^*
468270.bf2	468270bf2	[1, -1, 0, -96399, -2864295]	[2, 2]	4423680	\(\Gamma_0(N)\)-optimal^*
468270.bf1	468270bf3	[1, -1, 0, -913149, 333800055]	[2]	8847360	\(\Gamma_0(N)\)-optimal^*
468270.bf4	468270bf4	[1, -1, 0, 371871, -22812597]	[2]	8847360

^*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 468270bf1.

Rank

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

Complex multiplication

The elliptic curves in class 468270bf 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 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.