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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 163170.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 163170.co1 | 163170dl3 | \([1, -1, 0, -2326284, -1365077120]\) | \(16232905099479601/4052240\) | \(347544906161040\) | \([2]\) | \(2488320\) | \(2.1658\) | |
| 163170.co2 | 163170dl4 | \([1, -1, 0, -2317464, -1375948652]\) | \(-16048965315233521/256572640900\) | \(-22005240164718948900\) | \([2]\) | \(4976640\) | \(2.5123\) | |
| 163170.co3 | 163170dl1 | \([1, -1, 0, -33084, -1258160]\) | \(46694890801/18944000\) | \(1624753396224000\) | \([2]\) | \(829440\) | \(1.6165\) | \(\Gamma_0(N)\)-optimal |
| 163170.co4 | 163170dl2 | \([1, -1, 0, 108036, -9245552]\) | \(1625964918479/1369000000\) | \(-117413819649000000\) | \([2]\) | \(1658880\) | \(1.9630\) |
Rank
sage: E.rank()
The elliptic curves in class 163170.co have rank \(1\).
Complex multiplication
The elliptic curves in class 163170.co do not have complex multiplication.Modular form 163170.2.a.co
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
