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SageMath
E = EllipticCurve("gv1")
E.isogeny_class()
Elliptic curves in class 33600gv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.hb3 | 33600gv1 | \([0, 1, 0, -308, 1638]\) | \(3241792/567\) | \(567000000\) | \([2]\) | \(16384\) | \(0.39951\) | \(\Gamma_0(N)\)-optimal |
| 33600.hb2 | 33600gv2 | \([0, 1, 0, -1433, -19737]\) | \(5088448/441\) | \(28224000000\) | \([2, 2]\) | \(32768\) | \(0.74609\) | |
| 33600.hb4 | 33600gv3 | \([0, 1, 0, 1567, -88737]\) | \(830584/7203\) | \(-3687936000000\) | \([2]\) | \(65536\) | \(1.0927\) | |
| 33600.hb1 | 33600gv4 | \([0, 1, 0, -22433, -1300737]\) | \(2438569736/21\) | \(10752000000\) | \([2]\) | \(65536\) | \(1.0927\) |
Rank
sage: E.rank()
The elliptic curves in class 33600gv have rank \(0\).
Complex multiplication
The elliptic curves in class 33600gv do not have complex multiplication.Modular form 33600.2.a.gv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
