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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 323466bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
323466.bn2 | 323466bn1 | \([1, 0, 1, 69590647, 18057278540]\) | \(7721758769769063671471/4497774542859970944\) | \(-21709898643447393492237696\) | \([]\) | \(81134592\) | \(3.5511\) | \(\Gamma_0(N)\)-optimal |
323466.bn1 | 323466bn2 | \([1, 0, 1, -27554796143, -1760534950995520]\) | \(-479352730263827621784814619569/214316023050990383094\) | \(-1034462508906727840031567046\) | \([]\) | \(567942144\) | \(4.5240\) |
Rank
sage: E.rank()
The elliptic curves in class 323466bn have rank \(1\).
Complex multiplication
The elliptic curves in class 323466bn do not have complex multiplication.Modular form 323466.2.a.bn
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.