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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 115920.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.cl1 | 115920ep2 | \([0, 0, 0, -2082387, 1125007634]\) | \(334441811780708689/10434761366400\) | \(31158030483888537600\) | \([2]\) | \(3440640\) | \(2.5156\) | |
| 115920.cl2 | 115920ep1 | \([0, 0, 0, 37293, 59656466]\) | \(1920959458991/515997941760\) | \(-1540761598128291840\) | \([2]\) | \(1720320\) | \(2.1691\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.cl do not have complex multiplication.Modular form 115920.2.a.cl
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.
