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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 457776v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 457776.v2 | 457776v1 | \([0, 0, 0, -4849131, 3989798170]\) | \(35611289/1188\) | \(420672584155053441024\) | \([2]\) | \(20054016\) | \(2.7302\) | \(\Gamma_0(N)\)-optimal |
| 457776.v1 | 457776v2 | \([0, 0, 0, -11923851, -10322360390]\) | \(529475129/176418\) | \(62469878747025435992064\) | \([2]\) | \(40108032\) | \(3.0767\) |
Rank
sage: E.rank()
The elliptic curves in class 457776v have rank \(0\).
Complex multiplication
The elliptic curves in class 457776v do not have complex multiplication.Modular form 457776.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
