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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 61152.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61152.o1 | 61152bc2 | \([0, -1, 0, -1633, -8399]\) | \(1000000/507\) | \(244318384128\) | \([2]\) | \(46080\) | \(0.87764\) | |
61152.o2 | 61152bc1 | \([0, -1, 0, -898, 10564]\) | \(10648000/117\) | \(880955712\) | \([2]\) | \(23040\) | \(0.53107\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61152.o have rank \(1\).
Complex multiplication
The elliptic curves in class 61152.o do not have complex multiplication.Modular form 61152.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.