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SageMath
E = EllipticCurve("lm1")
E.isogeny_class()
Elliptic curves in class 381150.lm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.lm1 | 381150lm2 | \([1, -1, 1, -7637180, -1045603303]\) | \(19530306557/11114334\) | \(28034778042514933593750\) | \([2]\) | \(29491200\) | \(2.9972\) | |
381150.lm2 | 381150lm1 | \([1, -1, 1, 1891570, -130843303]\) | \(296740963/174636\) | \(-440501562957585937500\) | \([2]\) | \(14745600\) | \(2.6506\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 381150.lm have rank \(1\).
Complex multiplication
The elliptic curves in class 381150.lm do not have complex multiplication.Modular form 381150.2.a.lm
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.