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SageMath
E = EllipticCurve("rq1")
E.isogeny_class()
Elliptic curves in class 176400rq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.ce2 | 176400rq1 | \([0, 0, 0, -735, 17150]\) | \(-432\) | \(-101648736000\) | \([2]\) | \(147456\) | \(0.80045\) | \(\Gamma_0(N)\)-optimal |
| 176400.ce1 | 176400rq2 | \([0, 0, 0, -15435, 737450]\) | \(1000188\) | \(406594944000\) | \([2]\) | \(294912\) | \(1.1470\) |
Rank
sage: E.rank()
The elliptic curves in class 176400rq have rank \(1\).
Complex multiplication
The elliptic curves in class 176400rq do not have complex multiplication.Modular form 176400.2.a.rq
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.
