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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 82810.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82810.bn1 | 82810ba1 | \([1, -1, 0, -1090504, 438591908]\) | \(-5154200289/20\) | \(-556511867000180\) | \([]\) | \(1975680\) | \(2.0426\) | \(\Gamma_0(N)\)-optimal |
82810.bn2 | 82810ba2 | \([1, -1, 0, 7604546, -4160741740]\) | \(1747829720511/1280000000\) | \(-35616759488011520000000\) | \([]\) | \(13829760\) | \(3.0156\) |
Rank
sage: E.rank()
The elliptic curves in class 82810.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 82810.bn do not have complex multiplication.Modular form 82810.2.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 LMFDB 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 LMFDB labels.