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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 9075.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9075.q1 | 9075k3 | \([1, 0, 1, -443226, -113501027]\) | \(347873904937/395307\) | \(10942351003546875\) | \([2]\) | \(92160\) | \(1.9910\) | |
| 9075.q2 | 9075k2 | \([1, 0, 1, -34851, -789527]\) | \(169112377/88209\) | \(2441681628890625\) | \([2, 2]\) | \(46080\) | \(1.6445\) | |
| 9075.q3 | 9075k1 | \([1, 0, 1, -19726, 1055723]\) | \(30664297/297\) | \(8221150265625\) | \([2]\) | \(23040\) | \(1.2979\) | \(\Gamma_0(N)\)-optimal |
| 9075.q4 | 9075k4 | \([1, 0, 1, 131524, -6113527]\) | \(9090072503/5845851\) | \(-161816900678296875\) | \([2]\) | \(92160\) | \(1.9910\) |
Rank
sage: E.rank()
The elliptic curves in class 9075.q have rank \(1\).
Complex multiplication
The elliptic curves in class 9075.q do not have complex multiplication.Modular form 9075.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
