Show commands:
SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 480240ds
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 480240.ds2 | 480240ds1 | \([0, 0, 0, -17859072, 25884492464]\) | \(210966209738334797824/25153051046653125\) | \(75106607976489484800000\) | \([]\) | \(37324800\) | \(3.1204\) | \(\Gamma_0(N)\)-optimal |
| 480240.ds1 | 480240ds2 | \([0, 0, 0, -342584832, -2436912793744]\) | \(1489157481162281146384384/2616603057861328125\) | \(7813134865125000000000000\) | \([]\) | \(111974400\) | \(3.6697\) |
Rank
sage: E.rank()
The elliptic curves in class 480240ds have rank \(0\).
Complex multiplication
The elliptic curves in class 480240ds do not have complex multiplication.Modular form 480240.2.a.ds
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
