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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 388416dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.dd2 | 388416dd1 | \([0, -1, 0, 1685063, 18537145]\) | \(5352028359488/3098832471\) | \(-306373765481279483904\) | \([2]\) | \(13271040\) | \(2.6204\) | \(\Gamma_0(N)\)-optimal |
| 388416.dd1 | 388416dd2 | \([0, -1, 0, -6742177, 155058433]\) | \(42852953779784/24786408969\) | \(19604558864431722037248\) | \([2]\) | \(26542080\) | \(2.9670\) |
Rank
sage: E.rank()
The elliptic curves in class 388416dd have rank \(0\).
Complex multiplication
The elliptic curves in class 388416dd do not have complex multiplication.Modular form 388416.2.a.dd
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.
