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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 180336de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180336.br2 | 180336de1 | \([0, -1, 0, -15991, -572402]\) | \(1171019776/304317\) | \(117527561365968\) | \([2]\) | \(589824\) | \(1.4089\) | \(\Gamma_0(N)\)-optimal |
| 180336.br1 | 180336de2 | \([0, -1, 0, -237076, -44347232]\) | \(238481570896/25857\) | \(159776031138048\) | \([2]\) | \(1179648\) | \(1.7554\) |
Rank
sage: E.rank()
The elliptic curves in class 180336de have rank \(1\).
Complex multiplication
The elliptic curves in class 180336de do not have complex multiplication.Modular form 180336.2.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.
