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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 262080j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262080.j2 | 262080j1 | \([0, 0, 0, -3468, 23312]\) | \(24137569/12740\) | \(2434651914240\) | \([2]\) | \(294912\) | \(1.0683\) | \(\Gamma_0(N)\)-optimal |
262080.j1 | 262080j2 | \([0, 0, 0, -43788, 3523088]\) | \(48587168449/59150\) | \(11303741030400\) | \([2]\) | \(589824\) | \(1.4149\) |
Rank
sage: E.rank()
The elliptic curves in class 262080j have rank \(1\).
Complex multiplication
The elliptic curves in class 262080j do not have complex multiplication.Modular form 262080.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.