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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 150858.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
150858.o1 | 150858bh2 | \([1, -1, 0, -1183509, 499226841]\) | \(-10418796526321/82044596\) | \(-1443680323732773396\) | \([]\) | \(2496000\) | \(2.3131\) | |
150858.o2 | 150858bh1 | \([1, -1, 0, 12951, -945459]\) | \(13651919/29696\) | \(-522539362538496\) | \([]\) | \(499200\) | \(1.5084\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 150858.o have rank \(0\).
Complex multiplication
The elliptic curves in class 150858.o do not have complex multiplication.Modular form 150858.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.