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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 23400bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23400.bb1 | 23400bm1 | \([0, 0, 0, -146550, -20286875]\) | \(1909913257984/129730653\) | \(23643411509250000\) | \([2]\) | \(153600\) | \(1.8904\) | \(\Gamma_0(N)\)-optimal |
23400.bb2 | 23400bm2 | \([0, 0, 0, 126825, -87263750]\) | \(77366117936/1172914587\) | \(-3420218935692000000\) | \([2]\) | \(307200\) | \(2.2370\) |
Rank
sage: E.rank()
The elliptic curves in class 23400bm have rank \(0\).
Complex multiplication
The elliptic curves in class 23400bm do not have complex multiplication.Modular form 23400.2.a.bm
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.