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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 11830j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11830.f1 | 11830j1 | \([1, -1, 0, -9749, -334047]\) | \(9663597/980\) | \(10392409385540\) | \([2]\) | \(29952\) | \(1.2336\) | \(\Gamma_0(N)\)-optimal |
11830.f2 | 11830j2 | \([1, -1, 0, 12221, -1639065]\) | \(19034163/120050\) | \(-1273070149728650\) | \([2]\) | \(59904\) | \(1.5802\) |
Rank
sage: E.rank()
The elliptic curves in class 11830j have rank \(1\).
Complex multiplication
The elliptic curves in class 11830j do not have complex multiplication.Modular form 11830.2.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.