Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 180336bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
180336.bp2 | 180336bw1 | \([0, -1, 0, -1541, -20412]\) | \(1048576/117\) | \(45185529168\) | \([2]\) | \(245760\) | \(0.77751\) | \(\Gamma_0(N)\)-optimal |
180336.bp1 | 180336bw2 | \([0, -1, 0, -5876, 152988]\) | \(3631696/507\) | \(3132863355648\) | \([2]\) | \(491520\) | \(1.1241\) |
Rank
sage: E.rank()
The elliptic curves in class 180336bw have rank \(1\).
Complex multiplication
The elliptic curves in class 180336bw do not have complex multiplication.Modular form 180336.2.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 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.