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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 90354b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90354.e3 | 90354b1 | \([1, 1, 0, -11979, -510867]\) | \(-3753503985421/10392624\) | \(-526417583472\) | \([2]\) | \(230400\) | \(1.1221\) | \(\Gamma_0(N)\)-optimal |
| 90354.e2 | 90354b2 | \([1, 1, 0, -191799, -32410935]\) | \(15404978391891661/117612\) | \(5957400636\) | \([2]\) | \(460800\) | \(1.4686\) | |
| 90354.e4 | 90354b3 | \([1, 1, 0, 86256, 9153792]\) | \(1401130594505699/1519867920384\) | \(-76985869771210752\) | \([2]\) | \(1152000\) | \(1.9268\) | |
| 90354.e1 | 90354b4 | \([1, 1, 0, -482064, 84967680]\) | \(244587381607181341/79679768374272\) | \(4036019307461999616\) | \([2]\) | \(2304000\) | \(2.2734\) |
Rank
sage: E.rank()
The elliptic curves in class 90354b have rank \(0\).
Complex multiplication
The elliptic curves in class 90354b do not have complex multiplication.Modular form 90354.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
