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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 50715o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50715.bk1 | 50715o1 | \([1, -1, 0, -71745, -7376104]\) | \(476196576129/197225\) | \(16915223214225\) | \([2]\) | \(221184\) | \(1.5002\) | \(\Gamma_0(N)\)-optimal |
| 50715.bk2 | 50715o2 | \([1, -1, 0, -60720, -9728839]\) | \(-288673724529/311181605\) | \(-26688839187404205\) | \([2]\) | \(442368\) | \(1.8468\) |
Rank
sage: E.rank()
The elliptic curves in class 50715o have rank \(1\).
Complex multiplication
The elliptic curves in class 50715o do not have complex multiplication.Modular form 50715.2.a.o
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 Cremona 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 Cremona labels.
