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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 360789.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
360789.n1 | 360789n2 | \([1, 1, 0, -5944205, -4735698732]\) | \(39049652632434625/6327356209317\) | \(3763659033575909081757\) | \([2]\) | \(17310720\) | \(2.8620\) | |
360789.n2 | 360789n1 | \([1, 1, 0, 670260, -413807301]\) | \(55984089431375/156929368167\) | \(-93345247935526622607\) | \([2]\) | \(8655360\) | \(2.5154\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 360789.n have rank \(0\).
Complex multiplication
The elliptic curves in class 360789.n do not have complex multiplication.Modular form 360789.2.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 LMFDB 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 LMFDB labels.