Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 76230.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76230.bw1 | 76230k1 | \([1, -1, 0, -2532129, -1550045315]\) | \(37537160298467283/5519360000\) | \(264002838865920000\) | \([2]\) | \(1720320\) | \(2.3571\) | \(\Gamma_0(N)\)-optimal |
76230.bw2 | 76230k2 | \([1, -1, 0, -2299809, -1846160387]\) | \(-28124139978713043/14526050000000\) | \(-694812158929350000000\) | \([2]\) | \(3440640\) | \(2.7037\) |
Rank
sage: E.rank()
The elliptic curves in class 76230.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 76230.bw do not have complex multiplication.Modular form 76230.2.a.bw
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.