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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 364650.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.o1 | 364650o2 | \([1, 1, 0, -11442775, 12983255125]\) | \(10604686171605110456689/1473064877856000000\) | \(23016638716500000000000\) | \([2]\) | \(34062336\) | \(3.0174\) | |
364650.o2 | 364650o1 | \([1, 1, 0, -2994775, -1792296875]\) | \(190106300204077220209/21324397805568000\) | \(333193715712000000000\) | \([2]\) | \(17031168\) | \(2.6708\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364650.o have rank \(0\).
Complex multiplication
The elliptic curves in class 364650.o do not have complex multiplication.Modular form 364650.2.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.