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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 101568.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101568.dd1 | 101568dm2 | \([0, 1, 0, -1930497, 1010100735]\) | \(3370318/81\) | \(19122535213105545216\) | \([2]\) | \(3391488\) | \(2.4844\) | |
| 101568.dd2 | 101568dm1 | \([0, 1, 0, 16223, 49589087]\) | \(4/9\) | \(-1062363067394752512\) | \([2]\) | \(1695744\) | \(2.1379\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101568.dd have rank \(0\).
Complex multiplication
The elliptic curves in class 101568.dd do not have complex multiplication.Modular form 101568.2.a.dd
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.
