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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 17640.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17640.bm1 | 17640bv1 | \([0, 0, 0, -11907, -240786]\) | \(78732/35\) | \(82994159969280\) | \([2]\) | \(55296\) | \(1.3664\) | \(\Gamma_0(N)\)-optimal |
| 17640.bm2 | 17640bv2 | \([0, 0, 0, 41013, -1796634]\) | \(1608714/1225\) | \(-5809591197849600\) | \([2]\) | \(110592\) | \(1.7130\) |
Rank
sage: E.rank()
The elliptic curves in class 17640.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 17640.bm do not have complex multiplication.Modular form 17640.2.a.bm
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.
