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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 44100.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.a1 | 44100dt2 | \([0, 0, 0, -13377000, -18831557500]\) | \(-30866268160/3\) | \(-25729836300000000\) | \([]\) | \(1632960\) | \(2.5822\) | |
44100.a2 | 44100dt1 | \([0, 0, 0, -147000, -31727500]\) | \(-40960/27\) | \(-231568526700000000\) | \([]\) | \(544320\) | \(2.0329\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44100.a have rank \(1\).
Complex multiplication
The elliptic curves in class 44100.a do not have complex multiplication.Modular form 44100.2.a.a
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.