Show commands: SageMath
Rank
The elliptic curves in class 705600.bwv have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.bwv do not have complex multiplication.Modular form 705600.2.a.bwv
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
The vertices are labelled with LMFDB labels.
Elliptic curves in class 705600.bwv
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.bwv1 | \([0, 0, 0, -462182700, 3824361506000]\) | \(62161150998242/1607445\) | \(282346132215490560000000\) | \([2]\) | \(150994944\) | \(3.6065\) |
| 705600.bwv2 | \([0, 0, 0, -30002700, 54887546000]\) | \(34008619684/4862025\) | \(427004953041945600000000\) | \([2, 2]\) | \(75497472\) | \(3.2599\) |
| 705600.bwv3 | \([0, 0, 0, -7952700, -7778554000]\) | \(2533446736/275625\) | \(6051657497760000000000\) | \([2, 2]\) | \(37748736\) | \(2.9133\) |
| 705600.bwv4 | \([0, 0, 0, -7732200, -8275561000]\) | \(37256083456/525\) | \(720435416400000000\) | \([2]\) | \(18874368\) | \(2.5667\) |
| 705600.bwv5 | \([0, 0, 0, 10569300, -38636206000]\) | \(1486779836/8203125\) | \(-720435416400000000000000\) | \([2]\) | \(75497472\) | \(3.2599\) |
| 705600.bwv6 | \([0, 0, 0, 49377300, 296043986000]\) | \(75798394558/259416045\) | \(-45566172989053839360000000\) | \([2]\) | \(150994944\) | \(3.6065\) |