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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 48510f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.ba1 | 48510f1 | \([1, -1, 0, -115845, -15144319]\) | \(74246873427/16940\) | \(39227708422980\) | \([2]\) | \(294912\) | \(1.6002\) | \(\Gamma_0(N)\)-optimal |
| 48510.ba2 | 48510f2 | \([1, -1, 0, -102615, -18745525]\) | \(-51603494067/35870450\) | \(-83064672585660150\) | \([2]\) | \(589824\) | \(1.9467\) |
Rank
sage: E.rank()
The elliptic curves in class 48510f have rank \(1\).
Complex multiplication
The elliptic curves in class 48510f do not have complex multiplication.Modular form 48510.2.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.
