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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 54150.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54150.l1 | 54150g2 | \([1, 1, 0, -18036650, 29413612500]\) | \(882774443450089/2166000000\) | \(1592209035093750000000\) | \([2]\) | \(5806080\) | \(2.9465\) | |
| 54150.l2 | 54150g1 | \([1, 1, 0, -708650, 805084500]\) | \(-53540005609/350208000\) | \(-257435060832000000000\) | \([2]\) | \(2903040\) | \(2.5999\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.l have rank \(0\).
Complex multiplication
The elliptic curves in class 54150.l do not have complex multiplication.Modular form 54150.2.a.l
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.
