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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 54150.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.w1 | 54150y2 | \([1, 0, 1, -24556, 2401898]\) | \(-1392225385/1316928\) | \(-1548900949339200\) | \([]\) | \(311040\) | \(1.6110\) | |
54150.w2 | 54150y1 | \([1, 0, 1, 2519, -56512]\) | \(1503815/2052\) | \(-2413453695300\) | \([]\) | \(103680\) | \(1.0617\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.w have rank \(1\).
Complex multiplication
The elliptic curves in class 54150.w do not have complex multiplication.Modular form 54150.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.