Show commands:
SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 9800.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9800.bn1 | 9800i2 | \([0, -1, 0, -294408, -43631188]\) | \(2185454/625\) | \(807072140000000000\) | \([2]\) | \(129024\) | \(2.1426\) | |
9800.bn2 | 9800i1 | \([0, -1, 0, 48592, -4529188]\) | \(19652/25\) | \(-16141442800000000\) | \([2]\) | \(64512\) | \(1.7960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9800.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 9800.bn do not have complex multiplication.Modular form 9800.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.