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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 254898.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254898.bv1 | 254898bv2 | \([1, -1, 0, -3571227, 312699883]\) | \(2433138625/1387778\) | \(2872958119720493445522\) | \([2]\) | \(10616832\) | \(2.8073\) | |
| 254898.bv2 | 254898bv1 | \([1, -1, 0, -2296737, -1333176503]\) | \(647214625/3332\) | \(6897858630781496868\) | \([2]\) | \(5308416\) | \(2.4607\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254898.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 254898.bv do not have complex multiplication.Modular form 254898.2.a.bv
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.
