Show commands:
SageMath
E = EllipticCurve("ix1")
E.isogeny_class()
Elliptic curves in class 705600.ix
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.ix1 | \([0, 0, 0, -4500846014700, 3675270815038186000]\) | \(229625675762164624948320008/9568125\) | \(420157934844480000000000\) | \([2]\) | \(7927234560\) | \(5.4335\) |
| 705600.ix2 | \([0, 0, 0, -281302889700, 57426100576936000]\) | \(448487713888272974160064/91549016015625\) | \(502515455041730025000000000000\) | \([2, 2]\) | \(3963617280\) | \(5.0870\) |
| 705600.ix3 | \([0, 0, 0, -280338422700, 57839426767654000]\) | \(-55486311952875723077768/801237030029296875\) | \(-35184123938392734375000000000000000\) | \([2]\) | \(7927234560\) | \(5.4335\) |
| 705600.ix4 | \([0, 0, 0, -17641723575, 890818691749000]\) | \(7079962908642659949376/100085966990454375\) | \(8583985155305315771229375000000\) | \([2]\) | \(1981808640\) | \(4.7404\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.ix have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.ix do not have complex multiplication.Modular form 705600.2.a.ix
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().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
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
