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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 259350.fv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259350.fv1 | 259350fv2 | \([1, 0, 0, -242963, -46115583]\) | \(101513598260088169/377613600\) | \(5900212500000\) | \([2]\) | \(1597440\) | \(1.6661\) | |
259350.fv2 | 259350fv1 | \([1, 0, 0, -14963, -743583]\) | \(-23711636464489/1513774080\) | \(-23652720000000\) | \([2]\) | \(798720\) | \(1.3196\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259350.fv have rank \(0\).
Complex multiplication
The elliptic curves in class 259350.fv do not have complex multiplication.Modular form 259350.2.a.fv
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.