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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 83790.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83790.u1 | 83790j2 | \([1, -1, 0, -343695, 74974325]\) | \(1413487789441083/55278125000\) | \(175592235459375000\) | \([2]\) | \(1179648\) | \(2.0761\) | |
83790.u2 | 83790j1 | \([1, -1, 0, -55575, -3451939]\) | \(5976054062523/1824760000\) | \(5796392109480000\) | \([2]\) | \(589824\) | \(1.7295\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83790.u have rank \(1\).
Complex multiplication
The elliptic curves in class 83790.u do not have complex multiplication.Modular form 83790.2.a.u
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.