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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 376768bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 376768.bv4 | 376768bv1 | \([0, 0, 0, -87464, 975560]\) | \(121485312/69629\) | \(42410959890338816\) | \([2]\) | \(2365440\) | \(1.8802\) | \(\Gamma_0(N)\)-optimal |
| 376768.bv2 | 376768bv2 | \([0, 0, 0, -911644, -333641520]\) | \(8597884752/41209\) | \(401605824267698176\) | \([2, 2]\) | \(4730880\) | \(2.2268\) | |
| 376768.bv3 | 376768bv3 | \([0, 0, 0, -440684, -677819088]\) | \(-242793828/4950967\) | \(-193000284690933809152\) | \([2]\) | \(9461760\) | \(2.5733\) | |
| 376768.bv1 | 376768bv4 | \([0, 0, 0, -14569484, -21404957072]\) | \(8773811642628/203\) | \(7913415256506368\) | \([2]\) | \(9461760\) | \(2.5733\) |
Rank
sage: E.rank()
The elliptic curves in class 376768bv have rank \(0\).
Complex multiplication
The elliptic curves in class 376768bv do not have complex multiplication.Modular form 376768.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
