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SageMath
E = EllipticCurve("qp1")
E.isogeny_class()
Elliptic curves in class 176400qp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.sj2 | 176400qp1 | \([0, 0, 0, 437325, -121850750]\) | \(19652/25\) | \(-11767111801200000000\) | \([2]\) | \(3096576\) | \(2.3453\) | \(\Gamma_0(N)\)-optimal |
| 176400.sj1 | 176400qp2 | \([0, 0, 0, -2649675, -1180691750]\) | \(2185454/625\) | \(588355590060000000000\) | \([2]\) | \(6193152\) | \(2.6919\) |
Rank
sage: E.rank()
The elliptic curves in class 176400qp have rank \(1\).
Complex multiplication
The elliptic curves in class 176400qp do not have complex multiplication.Modular form 176400.2.a.qp
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.
