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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 180336.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
180336.o1 | 180336ct1 | \([0, -1, 0, -963, 5598]\) | \(256000/117\) | \(45185529168\) | \([2]\) | \(147456\) | \(0.73943\) | \(\Gamma_0(N)\)-optimal |
180336.o2 | 180336ct2 | \([0, -1, 0, 3372, 38544]\) | \(686000/507\) | \(-3132863355648\) | \([2]\) | \(294912\) | \(1.0860\) |
Rank
sage: E.rank()
The elliptic curves in class 180336.o have rank \(1\).
Complex multiplication
The elliptic curves in class 180336.o do not have complex multiplication.Modular form 180336.2.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.