Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 1710.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1710.t1 | 1710s4 | \([1, -1, 1, -11100992, 14238819299]\) | \(207530301091125281552569/805586668007040\) | \(587272680977132160\) | \([2]\) | \(71680\) | \(2.6227\) | |
| 1710.t2 | 1710s3 | \([1, -1, 1, -2103872, -906368029]\) | \(1412712966892699019449/330160465517040000\) | \(240686979361922160000\) | \([2]\) | \(71680\) | \(2.6227\) | |
| 1710.t3 | 1710s2 | \([1, -1, 1, -704192, 215615459]\) | \(52974743974734147769/3152005008998400\) | \(2297811651559833600\) | \([2, 2]\) | \(35840\) | \(2.2761\) | |
| 1710.t4 | 1710s1 | \([1, -1, 1, 33088, 13895651]\) | \(5495662324535111/117739817533440\) | \(-85832326981877760\) | \([4]\) | \(17920\) | \(1.9296\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1710.t have rank \(0\).
Complex multiplication
The elliptic curves in class 1710.t do not have complex multiplication.Modular form 1710.2.a.t
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.
