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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 135240db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 135240.y1 | 135240db1 | \([0, -1, 0, -155271020, 744755814132]\) | \(13745695765783090269904/148545140625\) | \(4473903935844000000\) | \([2]\) | \(11796480\) | \(3.1496\) | \(\Gamma_0(N)\)-optimal |
| 135240.y2 | 135240db2 | \([0, -1, 0, -155148520, 745989487132]\) | \(-3428296927707108677476/11297617307290125\) | \(-1361053059671424938112000\) | \([2]\) | \(23592960\) | \(3.4962\) |
Rank
sage: E.rank()
The elliptic curves in class 135240db have rank \(0\).
Complex multiplication
The elliptic curves in class 135240db do not have complex multiplication.Modular form 135240.2.a.db
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.
