Show commands:
SageMath
E = EllipticCurve("it1")
E.isogeny_class()
Elliptic curves in class 705600.it
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.it1 | \([0, 0, 0, -61740, -5899600]\) | \(1000188\) | \(26022076416000\) | \([2]\) | \(2359296\) | \(1.4936\) |
| 705600.it2 | \([0, 0, 0, -2940, -137200]\) | \(-432\) | \(-6505519104000\) | \([2]\) | \(1179648\) | \(1.1470\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.it have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.it do not have complex multiplication.Modular form 705600.2.a.it
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.
