Show commands:
SageMath
E = EllipticCurve("cbv1")
E.isogeny_class()
Elliptic curves in class 705600.cbv
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.cbv1 | \([0, 0, 0, -896700, -327026000]\) | \(-177953104/125\) | \(-56010528000000000\) | \([]\) | \(9953280\) | \(2.1500\) |
705600.cbv2 | \([0, 0, 0, 867300, -1388954000]\) | \(161017136/1953125\) | \(-875164500000000000000\) | \([]\) | \(29859840\) | \(2.6993\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.cbv have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.cbv do not have complex multiplication.Modular form 705600.2.a.cbv
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.