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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 90944.eg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90944.eg1 | 90944ca2 | \([0, -1, 0, -484577, -129673375]\) | \(408023180713/1421\) | \(43825031806976\) | \([2]\) | \(589824\) | \(1.8370\) | |
90944.eg2 | 90944ca1 | \([0, -1, 0, -29857, -2078943]\) | \(-95443993/5887\) | \(-181560846057472\) | \([2]\) | \(294912\) | \(1.4905\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 90944.eg have rank \(1\).
Complex multiplication
The elliptic curves in class 90944.eg do not have complex multiplication.Modular form 90944.2.a.eg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.