Show commands:
SageMath
E = EllipticCurve("ccc1")
E.isogeny_class()
Elliptic curves in class 705600.ccc
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.ccc1 | \([0, 0, 0, -85260, 9192400]\) | \(195112/9\) | \(3161682284544000\) | \([2]\) | \(4423680\) | \(1.7357\) |
705600.ccc2 | \([0, 0, 0, 2940, 548800]\) | \(64/3\) | \(-131736761856000\) | \([2]\) | \(2211840\) | \(1.3891\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.ccc have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.ccc do not have complex multiplication.Modular form 705600.2.a.ccc
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.