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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 10647.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10647.f1 | 10647c3 | \([0, 0, 1, -178464, 71519490]\) | \(-178643795968/524596891\) | \(-1845922037246247051\) | \([]\) | \(145152\) | \(2.1919\) | |
| 10647.f2 | 10647c1 | \([0, 0, 1, -11154, -454230]\) | \(-43614208/91\) | \(-320205682251\) | \([]\) | \(16128\) | \(1.0933\) | \(\Gamma_0(N)\)-optimal |
| 10647.f3 | 10647c2 | \([0, 0, 1, 19266, -2253573]\) | \(224755712/753571\) | \(-2651623254720531\) | \([]\) | \(48384\) | \(1.6426\) |
Rank
sage: E.rank()
The elliptic curves in class 10647.f have rank \(0\).
Complex multiplication
The elliptic curves in class 10647.f do not have complex multiplication.Modular form 10647.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
