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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 4830.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4830.r1 | 4830r1 | \([1, 1, 1, -1078221, 430483779]\) | \(138626767243242683688529/5300196249600\) | \(5300196249600\) | \([2]\) | \(46080\) | \(1.9328\) | \(\Gamma_0(N)\)-optimal |
| 4830.r2 | 4830r2 | \([1, 1, 1, -1076621, 431827139]\) | \(-138010547060620856386129/857302254769101120\) | \(-857302254769101120\) | \([2]\) | \(92160\) | \(2.2794\) |
Rank
sage: E.rank()
The elliptic curves in class 4830.r have rank \(1\).
Complex multiplication
The elliptic curves in class 4830.r do not have complex multiplication.Modular form 4830.2.a.r
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.
