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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 60840r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60840.a4 | 60840r1 | \([0, 0, 0, 5577, 74698]\) | \(21296/15\) | \(-13511976042240\) | \([2]\) | \(122880\) | \(1.2080\) | \(\Gamma_0(N)\)-optimal |
| 60840.a3 | 60840r2 | \([0, 0, 0, -24843, 628342]\) | \(470596/225\) | \(810718562534400\) | \([2, 2]\) | \(245760\) | \(1.5546\) | |
| 60840.a2 | 60840r3 | \([0, 0, 0, -207363, -35912162]\) | \(136835858/1875\) | \(13511976042240000\) | \([2]\) | \(491520\) | \(1.9012\) | |
| 60840.a1 | 60840r4 | \([0, 0, 0, -329043, 72602062]\) | \(546718898/405\) | \(2918586825123840\) | \([2]\) | \(491520\) | \(1.9012\) |
Rank
sage: E.rank()
The elliptic curves in class 60840r have rank \(0\).
Complex multiplication
The elliptic curves in class 60840r do not have complex multiplication.Modular form 60840.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
