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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 455175j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
455175.j2 | 455175j1 | \([0, 0, 1, -895305, -326065334]\) | \(886385087098880/21\) | \(1880327925\) | \([]\) | \(4761600\) | \(1.7521\) | \(\Gamma_0(N)\)-optimal* |
455175.j1 | 455175j2 | \([0, 0, 1, -1306875, 2935156]\) | \(7057510400/4084101\) | \(142846896555439453125\) | \([]\) | \(23808000\) | \(2.5568\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 455175j have rank \(0\).
Complex multiplication
The elliptic curves in class 455175j do not have complex multiplication.Modular form 455175.2.a.j
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.