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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 106560dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106560.j2 | 106560dt1 | \([0, 0, 0, -14744268, -21797934192]\) | \(-68700855708416547/24248320000\) | \(-125116005105008640000\) | \([2]\) | \(8110080\) | \(2.8262\) | \(\Gamma_0(N)\)-optimal |
| 106560.j1 | 106560dt2 | \([0, 0, 0, -235928268, -1394819732592]\) | \(281470209323873024547/35046400\) | \(180831726128332800\) | \([2]\) | \(16220160\) | \(3.1728\) |
Rank
sage: E.rank()
The elliptic curves in class 106560dt have rank \(1\).
Complex multiplication
The elliptic curves in class 106560dt do not have complex multiplication.Modular form 106560.2.a.dt
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.
