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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 44880bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44880.o2 | 44880bn1 | \([0, -1, 0, -1, 76]\) | \(-16384/154275\) | \(-2468400\) | \([2]\) | \(9600\) | \(-0.094498\) | \(\Gamma_0(N)\)-optimal |
44880.o1 | 44880bn2 | \([0, -1, 0, -276, 1836]\) | \(9115564624/143055\) | \(36622080\) | \([2]\) | \(19200\) | \(0.25208\) |
Rank
sage: E.rank()
The elliptic curves in class 44880bn have rank \(0\).
Complex multiplication
The elliptic curves in class 44880bn do not have complex multiplication.Modular form 44880.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.