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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 10350j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10350.u2 | 10350j1 | \([1, -1, 0, -342, -5184]\) | \(-389017/828\) | \(-9431437500\) | \([2]\) | \(8192\) | \(0.60290\) | \(\Gamma_0(N)\)-optimal |
10350.u1 | 10350j2 | \([1, -1, 0, -7092, -227934]\) | \(3463512697/3174\) | \(36153843750\) | \([2]\) | \(16384\) | \(0.94947\) |
Rank
sage: E.rank()
The elliptic curves in class 10350j have rank \(0\).
Complex multiplication
The elliptic curves in class 10350j do not have complex multiplication.Modular form 10350.2.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.