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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 76230n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76230.f2 | 76230n1 | \([1, -1, 0, -122535, 73011901]\) | \(-118370771/1270080\) | \(-2183196226267869120\) | \([2]\) | \(1216512\) | \(2.2010\) | \(\Gamma_0(N)\)-optimal |
76230.f1 | 76230n2 | \([1, -1, 0, -3476655, 2488649125]\) | \(2703627633491/9185400\) | \(15789186993544410600\) | \([2]\) | \(2433024\) | \(2.5476\) |
Rank
sage: E.rank()
The elliptic curves in class 76230n have rank \(0\).
Complex multiplication
The elliptic curves in class 76230n do not have complex multiplication.Modular form 76230.2.a.n
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.