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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 141120dp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.da1 | 141120dp1 | \([0, 0, 0, -9408, -128968]\) | \(1048576/525\) | \(46107866649600\) | \([2]\) | \(294912\) | \(1.3146\) | \(\Gamma_0(N)\)-optimal |
| 141120.da2 | 141120dp2 | \([0, 0, 0, 34692, -993328]\) | \(3286064/2205\) | \(-3098448638853120\) | \([2]\) | \(589824\) | \(1.6612\) |
Rank
sage: E.rank()
The elliptic curves in class 141120dp have rank \(0\).
Complex multiplication
The elliptic curves in class 141120dp do not have complex multiplication.Modular form 141120.2.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 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.
