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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 333270.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333270.u1 | 333270u2 | \([1, -1, 0, -4252500, -2252496200]\) | \(958839021545760503/307534384168200\) | \(2727750951235202772600\) | \([2]\) | \(19464192\) | \(2.8168\) | |
333270.u2 | 333270u1 | \([1, -1, 0, -3846780, -2902540784]\) | \(709748997075124343/136105583040\) | \(1207221542429958720\) | \([2]\) | \(9732096\) | \(2.4702\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333270.u have rank \(1\).
Complex multiplication
The elliptic curves in class 333270.u do not have complex multiplication.Modular form 333270.2.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.