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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 317322o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
317322.o2 | 317322o1 | \([1, -1, 0, -13059, -4429643]\) | \(-13997521/474336\) | \(-8346552770375136\) | \([]\) | \(2112000\) | \(1.7354\) | \(\Gamma_0(N)\)-optimal |
317322.o1 | 317322o2 | \([1, -1, 0, -1339569, 750354547]\) | \(-15107691357361/5067577806\) | \(-89170557528336144606\) | \([]\) | \(10560000\) | \(2.5401\) |
Rank
sage: E.rank()
The elliptic curves in class 317322o have rank \(0\).
Complex multiplication
The elliptic curves in class 317322o do not have complex multiplication.Modular form 317322.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.