Show commands:
SageMath
E = EllipticCurve("oc1")
E.isogeny_class()
Elliptic curves in class 705600.oc
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.oc1 | \([0, 0, 0, -49980, -3155600]\) | \(78608/21\) | \(3688629331968000\) | \([2]\) | \(3145728\) | \(1.6953\) |
705600.oc2 | \([0, 0, 0, 126420, -20442800]\) | \(318028/441\) | \(-309844863885312000\) | \([2]\) | \(6291456\) | \(2.0419\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.oc have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.oc do not have complex multiplication.Modular form 705600.2.a.oc
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.