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SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 215600gx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215600.ei1 | 215600gx1 | \([0, 0, 0, -46550, -3730125]\) | \(379275264/15125\) | \(444860281250000\) | \([2]\) | \(829440\) | \(1.5772\) | \(\Gamma_0(N)\)-optimal |
| 215600.ei2 | 215600gx2 | \([0, 0, 0, 20825, -13634250]\) | \(2122416/171875\) | \(-80883687500000000\) | \([2]\) | \(1658880\) | \(1.9238\) |
Rank
sage: E.rank()
The elliptic curves in class 215600gx have rank \(1\).
Complex multiplication
The elliptic curves in class 215600gx do not have complex multiplication.Modular form 215600.2.a.gx
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.
