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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 270641.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270641.b1 | 270641b3 | \([1, -1, 1, -207919, 36534880]\) | \(209267191953/55223\) | \(262315006500743\) | \([2]\) | \(1382400\) | \(1.7512\) | |
| 270641.b2 | 270641b2 | \([1, -1, 1, -14604, 423638]\) | \(72511713/25921\) | \(123127452030961\) | \([2, 2]\) | \(691200\) | \(1.4046\) | |
| 270641.b3 | 270641b1 | \([1, -1, 1, -6199, -181522]\) | \(5545233/161\) | \(764766782801\) | \([2]\) | \(345600\) | \(1.0580\) | \(\Gamma_0(N)\)-optimal |
| 270641.b4 | 270641b4 | \([1, -1, 1, 44231, 2941776]\) | \(2014698447/1958887\) | \(-9304917446339767\) | \([2]\) | \(1382400\) | \(1.7512\) |
Rank
sage: E.rank()
The elliptic curves in class 270641.b have rank \(1\).
Complex multiplication
The elliptic curves in class 270641.b do not have complex multiplication.Modular form 270641.2.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 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.
