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SageMath
E = EllipticCurve("nq1")
E.isogeny_class()
Elliptic curves in class 176400nq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.j1 | 176400nq1 | \([0, 0, 0, -9441075, -11147242750]\) | \(197723452/375\) | \(176506677018000000000\) | \([2]\) | \(10321920\) | \(2.7748\) | \(\Gamma_0(N)\)-optimal |
| 176400.j2 | 176400nq2 | \([0, 0, 0, -6354075, -18559129750]\) | \(-30138446/140625\) | \(-132380007763500000000000\) | \([2]\) | \(20643840\) | \(3.1213\) |
Rank
sage: E.rank()
The elliptic curves in class 176400nq have rank \(1\).
Complex multiplication
The elliptic curves in class 176400nq do not have complex multiplication.Modular form 176400.2.a.nq
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.
