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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 346560.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
346560.f1 | 346560f3 | \([0, -1, 0, -693601, 206553985]\) | \(11968836484/961875\) | \(2965651900784640000\) | \([2]\) | \(5898240\) | \(2.2877\) | |
346560.f2 | 346560f2 | \([0, -1, 0, -144881, -17433519]\) | \(436334416/81225\) | \(62608206794342400\) | \([2, 2]\) | \(2949120\) | \(1.9411\) | |
346560.f3 | 346560f1 | \([0, -1, 0, -137661, -19612515]\) | \(5988775936/285\) | \(13729869911040\) | \([2]\) | \(1474560\) | \(1.5945\) | \(\Gamma_0(N)\)-optimal |
346560.f4 | 346560f4 | \([0, -1, 0, 288319, -102080799]\) | \(859687196/1954815\) | \(-6027083374068695040\) | \([2]\) | \(5898240\) | \(2.2877\) |
Rank
sage: E.rank()
The elliptic curves in class 346560.f have rank \(1\).
Complex multiplication
The elliptic curves in class 346560.f do not have complex multiplication.Modular form 346560.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.