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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 35904.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35904.ba1 | 35904q1 | \([0, -1, 0, -57857, 5333505]\) | \(81706955619457/744505344\) | \(195167608897536\) | \([2]\) | \(215040\) | \(1.5643\) | \(\Gamma_0(N)\)-optimal |
| 35904.ba2 | 35904q2 | \([0, -1, 0, -16897, 12698113]\) | \(-2035346265217/264305213568\) | \(-69286025905569792\) | \([2]\) | \(430080\) | \(1.9109\) |
Rank
sage: E.rank()
The elliptic curves in class 35904.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 35904.ba do not have complex multiplication.Modular form 35904.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
