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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 346560.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.bh1 | 346560bh2 | \([0, -1, 0, -43041, -2041695]\) | \(4904335099/1822500\) | \(3276938280960000\) | \([2]\) | \(1474560\) | \(1.6771\) | |
| 346560.bh2 | 346560bh1 | \([0, -1, 0, -18721, 969121]\) | \(403583419/10800\) | \(19418893516800\) | \([2]\) | \(737280\) | \(1.3305\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 346560.bh do not have complex multiplication.Modular form 346560.2.a.bh
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.
