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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 345520bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
345520.bn2 | 345520bn1 | \([0, 0, 0, -2205307, -1279493206]\) | \(-289581579184798874961/5081260310000000\) | \(-20812842229760000000\) | \([]\) | \(20942208\) | \(2.5042\) | \(\Gamma_0(N)\)-optimal |
345520.bn1 | 345520bn2 | \([0, 0, 0, -20332507, 154395929354]\) | \(-226953328047600468451761/2382836194386693393110\) | \(-9760097052207896138178560\) | \([]\) | \(146595456\) | \(3.4772\) |
Rank
sage: E.rank()
The elliptic curves in class 345520bn have rank \(0\).
Complex multiplication
The elliptic curves in class 345520bn do not have complex multiplication.Modular form 345520.2.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.