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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 270480.da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.da1 | 270480da3 | \([0, -1, 0, -3960000, 3034400832]\) | \(14251520160844849/264449745\) | \(127435768010772480\) | \([4]\) | \(5898240\) | \(2.4071\) | |
| 270480.da2 | 270480da2 | \([0, -1, 0, -255600, 44209152]\) | \(3832302404449/472410225\) | \(227649906937958400\) | \([2, 2]\) | \(2949120\) | \(2.0606\) | |
| 270480.da3 | 270480da1 | \([0, -1, 0, -63520, -5424320]\) | \(58818484369/7455105\) | \(3592542814801920\) | \([2]\) | \(1474560\) | \(1.7140\) | \(\Gamma_0(N)\)-optimal |
| 270480.da4 | 270480da4 | \([0, -1, 0, 375520, 227486400]\) | \(12152722588271/53476250625\) | \(-25769686670461440000\) | \([2]\) | \(5898240\) | \(2.4071\) |
Rank
sage: E.rank()
The elliptic curves in class 270480.da have rank \(1\).
Complex multiplication
The elliptic curves in class 270480.da do not have complex multiplication.Modular form 270480.2.a.da
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
