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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 15680.dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.dm1 | 15680dr2 | \([0, -1, 0, -10145, -679615]\) | \(-8990558521/10485760\) | \(-134690174402560\) | \([]\) | \(48384\) | \(1.4052\) | |
| 15680.dm2 | 15680dr1 | \([0, -1, 0, 1055, 17025]\) | \(10100279/16000\) | \(-205520896000\) | \([]\) | \(16128\) | \(0.85594\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15680.dm have rank \(0\).
Complex multiplication
The elliptic curves in class 15680.dm do not have complex multiplication.Modular form 15680.2.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.
