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SageMath
E = EllipticCurve("gd1")
E.isogeny_class()
Elliptic curves in class 215600gd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215600.bo2 | 215600gd1 | \([0, 1, 0, 4688892, 4144313788]\) | \(24226243449392/29774625727\) | \(-14011819768623292000000\) | \([2]\) | \(11796480\) | \(2.9356\) | \(\Gamma_0(N)\)-optimal |
215600.bo1 | 215600gd2 | \([0, 1, 0, -27920608, 39819106788]\) | \(1278763167594532/375974556419\) | \(707728489410222896000000\) | \([2]\) | \(23592960\) | \(3.2822\) |
Rank
sage: E.rank()
The elliptic curves in class 215600gd have rank \(1\).
Complex multiplication
The elliptic curves in class 215600gd do not have complex multiplication.Modular form 215600.2.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.