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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 35904bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35904.ce3 | 35904bb1 | \([0, 1, 0, -529889, -133764225]\) | \(62768149033310713/6915442583808\) | \(1812841780689764352\) | \([2]\) | \(737280\) | \(2.2368\) | \(\Gamma_0(N)\)-optimal |
| 35904.ce2 | 35904bb2 | \([0, 1, 0, -2009569, 952616831]\) | \(3423676911662954233/483711578981136\) | \(126802088160430915584\) | \([2, 2]\) | \(1474560\) | \(2.5834\) | |
| 35904.ce4 | 35904bb3 | \([0, 1, 0, 3278111, 5124596351]\) | \(14861225463775641287/51859390496937804\) | \(-13594628062429263691776\) | \([2]\) | \(2949120\) | \(2.9300\) | |
| 35904.ce1 | 35904bb4 | \([0, 1, 0, -30972129, 66332699775]\) | \(12534210458299016895673/315581882565708\) | \(82727897023304957952\) | \([2]\) | \(2949120\) | \(2.9300\) |
Rank
sage: E.rank()
The elliptic curves in class 35904bb have rank \(0\).
Complex multiplication
The elliptic curves in class 35904bb do not have complex multiplication.Modular form 35904.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
