Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 2450.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2450.bb1 | 2450be2 | \([1, -1, 1, -170680, -27098053]\) | \(-5745702166029/8192\) | \(-784000000000\) | \([]\) | \(9360\) | \(1.5538\) | |
2450.bb2 | 2450be1 | \([1, -1, 1, -55, 697]\) | \(-189/2\) | \(-191406250\) | \([]\) | \(720\) | \(0.27128\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2450.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 2450.bb do not have complex multiplication.Modular form 2450.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.