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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 243360dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 243360.dn2 | 243360dn1 | \([0, 0, 0, -106977, -22339096]\) | \(-601211584/609375\) | \(-137231006679000000\) | \([2]\) | \(2580480\) | \(1.9839\) | \(\Gamma_0(N)\)-optimal |
| 243360.dn1 | 243360dn2 | \([0, 0, 0, -2008227, -1095024346]\) | \(497169541448/190125\) | \(342528592670784000\) | \([2]\) | \(5160960\) | \(2.3305\) |
Rank
sage: E.rank()
The elliptic curves in class 243360dn have rank \(1\).
Complex multiplication
The elliptic curves in class 243360dn do not have complex multiplication.Modular form 243360.2.a.dn
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.
