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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 169920.dp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169920.dp1 | 169920du2 | \([0, 0, 0, -695892, 223437386]\) | \(798806778238038016/10723864485\) | \(500332621412160\) | \([]\) | \(1280000\) | \(1.9634\) | |
| 169920.dp2 | 169920du1 | \([0, 0, 0, -10092, -383974]\) | \(2436396322816/44803125\) | \(2090334600000\) | \([]\) | \(256000\) | \(1.1587\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 169920.dp have rank \(1\).
Complex multiplication
The elliptic curves in class 169920.dp do not have complex multiplication.Modular form 169920.2.a.dp
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
