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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 159120de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159120.dr1 | 159120de1 | \([0, 0, 0, -2529147, 1545816314]\) | \(2396726313900986596/4154072495625\) | \(3100998501694080000\) | \([2]\) | \(2949120\) | \(2.4421\) | \(\Gamma_0(N)\)-optimal |
| 159120.dr2 | 159120de2 | \([0, 0, 0, -1738227, 2530195346]\) | \(-389032340685029858/1627263833203125\) | \(-2429491884861600000000\) | \([2]\) | \(5898240\) | \(2.7886\) |
Rank
sage: E.rank()
The elliptic curves in class 159120de have rank \(0\).
Complex multiplication
The elliptic curves in class 159120de do not have complex multiplication.Modular form 159120.2.a.de
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.
