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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 468270.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
468270.i1 | 468270i1 | \([1, -1, 0, -168280470, -838068878300]\) | \(408076159454905367161/1190206406250000\) | \(1537113450170476406250000\) | \([2]\) | \(91238400\) | \(3.5115\) | \(\Gamma_0(N)\)-optimal |
468270.i2 | 468270i2 | \([1, -1, 0, -100217970, -1522273965800]\) | \(-86193969101536367161/725294740213012500\) | \(-936694925069281880746612500\) | \([2]\) | \(182476800\) | \(3.8581\) |
Rank
sage: E.rank()
The elliptic curves in class 468270.i have rank \(0\).
Complex multiplication
The elliptic curves in class 468270.i do not have complex multiplication.Modular form 468270.2.a.i
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.