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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 277729.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277729.a1 | 277729a3 | \([1, -1, 1, -25186549, 48658333436]\) | \(82483294977/17\) | \(364177082744155313\) | \([2]\) | \(8709120\) | \(2.7570\) | |
| 277729.a2 | 277729a2 | \([1, -1, 1, -1579584, 755080058]\) | \(20346417/289\) | \(6191010406650640321\) | \([2, 2]\) | \(4354560\) | \(2.4104\) | |
| 277729.a3 | 277729a1 | \([1, -1, 1, -190939, -13673814]\) | \(35937/17\) | \(364177082744155313\) | \([2]\) | \(2177280\) | \(2.0638\) | \(\Gamma_0(N)\)-optimal |
| 277729.a4 | 277729a4 | \([1, -1, 1, -190939, 2035410748]\) | \(-35937/83521\) | \(-1789202007522035052769\) | \([2]\) | \(8709120\) | \(2.7570\) |
Rank
sage: E.rank()
The elliptic curves in class 277729.a have rank \(0\).
Complex multiplication
The elliptic curves in class 277729.a do not have complex multiplication.Modular form 277729.2.a.a
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.
