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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 190575v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.r2 | 190575v1 | \([1, -1, 1, -2192180, -1309005178]\) | \(-461889917/26411\) | \(-66619063533708984375\) | \([2]\) | \(5990400\) | \(2.5606\) | \(\Gamma_0(N)\)-optimal |
| 190575.r1 | 190575v2 | \([1, -1, 1, -35542805, -81550608928]\) | \(1968634623437/5929\) | \(14955299976955078125\) | \([2]\) | \(11980800\) | \(2.9071\) |
Rank
sage: E.rank()
The elliptic curves in class 190575v have rank \(2\).
Complex multiplication
The elliptic curves in class 190575v do not have complex multiplication.Modular form 190575.2.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.
