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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 377706u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
377706.u2 | 377706u1 | \([1, 1, 0, -11384, -660480]\) | \(-1102302937/616896\) | \(-91322747780544\) | \([2]\) | \(1182720\) | \(1.3821\) | \(\Gamma_0(N)\)-optimal |
377706.u1 | 377706u2 | \([1, 1, 0, -201824, -34977768]\) | \(6141556990297/1019592\) | \(150936208137288\) | \([2]\) | \(2365440\) | \(1.7287\) |
Rank
sage: E.rank()
The elliptic curves in class 377706u have rank \(0\).
Complex multiplication
The elliptic curves in class 377706u do not have complex multiplication.Modular form 377706.2.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 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.