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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 223440.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 223440.dn1 | 223440dx2 | \([0, -1, 0, -1268920, 550590832]\) | \(468898230633769/5540400\) | \(2669865040281600\) | \([2]\) | \(3317760\) | \(2.1101\) | |
| 223440.dn2 | 223440dx1 | \([0, -1, 0, -77240, 9091440]\) | \(-105756712489/12476160\) | \(-6012140535152640\) | \([2]\) | \(1658880\) | \(1.7635\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 223440.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 223440.dn do not have complex multiplication.Modular form 223440.2.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 LMFDB 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 LMFDB labels.
