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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 363090.dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363090.dv1 | 363090dv2 | \([1, 0, 1, -476208, 126445918]\) | \(101513598260088169/377613600\) | \(44425862426400\) | \([2]\) | \(3194880\) | \(1.8344\) | |
363090.dv2 | 363090dv1 | \([1, 0, 1, -29328, 2034526]\) | \(-23711636464489/1513774080\) | \(-178094006737920\) | \([2]\) | \(1597440\) | \(1.4878\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363090.dv have rank \(0\).
Complex multiplication
The elliptic curves in class 363090.dv do not have complex multiplication.Modular form 363090.2.a.dv
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.