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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 4410.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4410.r1 | 4410n1 | \([1, -1, 0, -58074, -5372200]\) | \(-5154200289/20\) | \(-84050798580\) | \([]\) | \(11760\) | \(1.3094\) | \(\Gamma_0(N)\)-optimal |
| 4410.r2 | 4410n2 | \([1, -1, 0, 404976, 51008768]\) | \(1747829720511/1280000000\) | \(-5379251109120000000\) | \([]\) | \(82320\) | \(2.2824\) |
Rank
sage: E.rank()
The elliptic curves in class 4410.r have rank \(1\).
Complex multiplication
The elliptic curves in class 4410.r do not have complex multiplication.Modular form 4410.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
