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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 455175o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
455175.o2 | 455175o1 | \([0, 0, 1, -258743145, -1601958984714]\) | \(886385087098880/21\) | \(45386545032314325\) | \([]\) | \(80947200\) | \(3.1687\) | \(\Gamma_0(N)\)-optimal* |
455175.o1 | 455175o2 | \([0, 0, 1, -377686875, 14420422656]\) | \(7057510400/4084101\) | \(3447976822042782125126953125\) | \([]\) | \(404736000\) | \(3.9734\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 455175o have rank \(1\).
Complex multiplication
The elliptic curves in class 455175o do not have complex multiplication.Modular form 455175.2.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 Cremona 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 Cremona labels.