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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 91035.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91035.t1 | 91035bj4 | \([1, -1, 1, -773852, -255808996]\) | \(2912566550041/76531875\) | \(1346676898450156875\) | \([2]\) | \(1179648\) | \(2.2601\) | |
| 91035.t2 | 91035bj2 | \([1, -1, 1, -110597, 8431796]\) | \(8502154921/3186225\) | \(56065732098741225\) | \([2, 2]\) | \(589824\) | \(1.9135\) | |
| 91035.t3 | 91035bj1 | \([1, -1, 1, -97592, 11755874]\) | \(5841725401/1785\) | \(31409373724785\) | \([4]\) | \(294912\) | \(1.5669\) | \(\Gamma_0(N)\)-optimal |
| 91035.t4 | 91035bj3 | \([1, -1, 1, 344578, 59775536]\) | \(257138126279/236782035\) | \(-4166484833966455035\) | \([2]\) | \(1179648\) | \(2.2601\) |
Rank
sage: E.rank()
The elliptic curves in class 91035.t have rank \(1\).
Complex multiplication
The elliptic curves in class 91035.t do not have complex multiplication.Modular form 91035.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
