Show commands:
SageMath
E = EllipticCurve("hn1")
E.isogeny_class()
Elliptic curves in class 176400hn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.fq1 | 176400hn1 | \([0, 0, 0, -23229675, 43093748250]\) | \(-5154200289/20\) | \(-5379251109120000000\) | \([]\) | \(6773760\) | \(2.8073\) | \(\Gamma_0(N)\)-optimal |
| 176400.fq2 | 176400hn2 | \([0, 0, 0, 161990325, -408880095750]\) | \(1747829720511/1280000000\) | \(-344272070983680000000000000\) | \([]\) | \(47416320\) | \(3.7803\) |
Rank
sage: E.rank()
The elliptic curves in class 176400hn have rank \(1\).
Complex multiplication
The elliptic curves in class 176400hn do not have complex multiplication.Modular form 176400.2.a.hn
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
