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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 159120.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159120.f1 | 159120be1 | \([0, 0, 0, -588, -5137]\) | \(1927561216/138125\) | \(1611090000\) | \([2]\) | \(64512\) | \(0.51354\) | \(\Gamma_0(N)\)-optimal |
| 159120.f2 | 159120be2 | \([0, 0, 0, 537, -22462]\) | \(91765424/1221025\) | \(-227872569600\) | \([2]\) | \(129024\) | \(0.86011\) |
Rank
sage: E.rank()
The elliptic curves in class 159120.f have rank \(1\).
Complex multiplication
The elliptic curves in class 159120.f do not have complex multiplication.Modular form 159120.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
