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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 491970m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
491970.m2 | 491970m1 | \([1, 1, 0, -25667, -839811]\) | \(12633057289/5304720\) | \(785288941096080\) | \([2]\) | \(2568192\) | \(1.5550\) | \(\Gamma_0(N)\)-optimal |
491970.m1 | 491970m2 | \([1, 1, 0, -353647, -81063719]\) | \(33042169120969/14759100\) | \(2184876489339900\) | \([2]\) | \(5136384\) | \(1.9016\) |
Rank
sage: E.rank()
The elliptic curves in class 491970m have rank \(0\).
Complex multiplication
The elliptic curves in class 491970m do not have complex multiplication.Modular form 491970.2.a.m
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.