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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 122304de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122304.hu2 | 122304de1 | \([0, 1, 0, -30592, 3314870]\) | \(-420526439488/390971529\) | \(-2943834202580544\) | \([2]\) | \(552960\) | \(1.6648\) | \(\Gamma_0(N)\)-optimal |
| 122304.hu1 | 122304de2 | \([0, 1, 0, -568857, 164902023]\) | \(42246001231552/14414517\) | \(6946215979143168\) | \([2]\) | \(1105920\) | \(2.0113\) |
Rank
sage: E.rank()
The elliptic curves in class 122304de have rank \(1\).
Complex multiplication
The elliptic curves in class 122304de do not have complex multiplication.Modular form 122304.2.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.
