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SageMath
E = EllipticCurve("pg1")
E.isogeny_class()
Elliptic curves in class 176400pg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.kr1 | 176400pg1 | \([0, 0, 0, -565950, -123951625]\) | \(2725888/675\) | \(4964250291131250000\) | \([2]\) | \(2064384\) | \(2.2977\) | \(\Gamma_0(N)\)-optimal |
| 176400.kr2 | 176400pg2 | \([0, 0, 0, 1363425, -785727250]\) | \(2382032/3645\) | \(-428911225153740000000\) | \([2]\) | \(4128768\) | \(2.6443\) |
Rank
sage: E.rank()
The elliptic curves in class 176400pg have rank \(1\).
Complex multiplication
The elliptic curves in class 176400pg do not have complex multiplication.Modular form 176400.2.a.pg
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.
