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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 77760.dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77760.dm1 | 77760br2 | \([0, 0, 0, -700812, 225813744]\) | \(819699324507/80\) | \(3715041853440\) | \([]\) | \(497664\) | \(1.8450\) | |
| 77760.dm2 | 77760br1 | \([0, 0, 0, -9612, 236784]\) | \(1541767203/512000\) | \(32614907904000\) | \([]\) | \(165888\) | \(1.2957\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 77760.dm have rank \(1\).
Complex multiplication
The elliptic curves in class 77760.dm do not have complex multiplication.Modular form 77760.2.a.dm
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
