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SageMath
E = EllipticCurve("ij1")
E.isogeny_class()
Elliptic curves in class 73920.ij
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.ij1 | 73920ii4 | \([0, 1, 0, -1666785, -828754785]\) | \(1953542217204454969/170843779260\) | \(44785671670333440\) | \([2]\) | \(983040\) | \(2.2363\) | |
| 73920.ij2 | 73920ii3 | \([0, 1, 0, -604385, 171403935]\) | \(93137706732176569/5369647977540\) | \(1407620999424245760\) | \([2]\) | \(983040\) | \(2.2363\) | |
| 73920.ij3 | 73920ii2 | \([0, 1, 0, -111585, -11030625]\) | \(586145095611769/140040608400\) | \(36710805248409600\) | \([2, 2]\) | \(491520\) | \(1.8898\) | |
| 73920.ij4 | 73920ii1 | \([0, 1, 0, 16415, -1072225]\) | \(1865864036231/2993760000\) | \(-784796221440000\) | \([2]\) | \(245760\) | \(1.5432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.ij have rank \(0\).
Complex multiplication
The elliptic curves in class 73920.ij do not have complex multiplication.Modular form 73920.2.a.ij
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
