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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 14504f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14504.b2 | 14504f1 | \([0, 1, 0, 768, 362032]\) | \(415292/469567\) | \(-56569946094592\) | \([2]\) | \(41472\) | \(1.3179\) | \(\Gamma_0(N)\)-optimal |
| 14504.b1 | 14504f2 | \([0, 1, 0, -71752, 7207920]\) | \(169556172914/4353013\) | \(1048837378942976\) | \([2]\) | \(82944\) | \(1.6644\) |
Rank
sage: E.rank()
The elliptic curves in class 14504f have rank \(0\).
Complex multiplication
The elliptic curves in class 14504f do not have complex multiplication.Modular form 14504.2.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 Cremona 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 Cremona labels.
