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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 16245.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16245.d1 | 16245l2 | \([1, -1, 1, -246992, -2283816]\) | \(48587168449/28048275\) | \(961956183962945475\) | \([2]\) | \(230400\) | \(2.1402\) | |
| 16245.d2 | 16245l1 | \([1, -1, 1, 61663, -308424]\) | \(756058031/438615\) | \(-15042936210120135\) | \([2]\) | \(115200\) | \(1.7936\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16245.d have rank \(0\).
Complex multiplication
The elliptic curves in class 16245.d do not have complex multiplication.Modular form 16245.2.a.d
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.
