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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 13520y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13520.k2 | 13520y1 | \([0, -1, 0, -1070, 13207]\) | \(296747776/15625\) | \(7140250000\) | \([]\) | \(6912\) | \(0.64776\) | \(\Gamma_0(N)\)-optimal |
| 13520.k1 | 13520y2 | \([0, -1, 0, -85570, 9663107]\) | \(151635187115776/25\) | \(11424400\) | \([]\) | \(20736\) | \(1.1971\) |
Rank
sage: E.rank()
The elliptic curves in class 13520y have rank \(1\).
Complex multiplication
The elliptic curves in class 13520y do not have complex multiplication.Modular form 13520.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
