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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 152592.de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152592.de1 | 152592bd2 | \([0, 1, 0, -760589752, 8073468943700]\) | \(2418067440128989194388361/8359273562112\) | \(168219078699648024576\) | \([2]\) | \(39223296\) | \(3.5248\) | |
| 152592.de2 | 152592bd1 | \([0, 1, 0, -47558072, 126017838420]\) | \(591139158854005457801/1097587482427392\) | \(22087464145575022166016\) | \([2]\) | \(19611648\) | \(3.1782\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152592.de have rank \(1\).
Complex multiplication
The elliptic curves in class 152592.de do not have complex multiplication.Modular form 152592.2.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 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.
