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SageMath
E = EllipticCurve("gd1")
E.isogeny_class()
Elliptic curves in class 259182.gd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259182.gd1 | 259182gd1 | \([1, -1, 1, -221, 1829]\) | \(-13475473/7616\) | \(-671799744\) | \([]\) | \(120960\) | \(0.39693\) | \(\Gamma_0(N)\)-optimal |
259182.gd2 | 259182gd2 | \([1, -1, 1, 1759, -24307]\) | \(6827155247/6740636\) | \(-594584760924\) | \([]\) | \(362880\) | \(0.94624\) |
Rank
sage: E.rank()
The elliptic curves in class 259182.gd have rank \(0\).
Complex multiplication
The elliptic curves in class 259182.gd do not have complex multiplication.Modular form 259182.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.