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SageMath
E = EllipticCurve("bnl1")
E.isogeny_class()
Elliptic curves in class 705600.bnl
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.bnl1 | \([0, 0, 0, -1161300, -474712000]\) | \(31554496/525\) | \(2881741665600000000\) | \([2]\) | \(14155776\) | \(2.3406\) |
| 705600.bnl2 | \([0, 0, 0, -3675, -20923000]\) | \(-64/2205\) | \(-189114296805000000\) | \([2]\) | \(7077888\) | \(1.9940\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bnl have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.bnl do not have complex multiplication.Modular form 705600.2.a.bnl
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.
