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SageMath
E = EllipticCurve("gd1")
E.isogeny_class()
Elliptic curves in class 33600gd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.ef2 | 33600gd1 | \([0, 1, 0, -8, -2262]\) | \(-64/2205\) | \(-2205000000\) | \([2]\) | \(18432\) | \(0.47173\) | \(\Gamma_0(N)\)-optimal |
| 33600.ef1 | 33600gd2 | \([0, 1, 0, -2633, -52137]\) | \(31554496/525\) | \(33600000000\) | \([2]\) | \(36864\) | \(0.81830\) |
Rank
sage: E.rank()
The elliptic curves in class 33600gd have rank \(1\).
Complex multiplication
The elliptic curves in class 33600gd do not have complex multiplication.Modular form 33600.2.a.gd
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.
