Show commands:
SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 304704.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304704.bz1 | 304704bz2 | \([0, 0, 0, -4292076, 3422545360]\) | \(15043017316604/243\) | \(141252856971264\) | \([2]\) | \(5898240\) | \(2.2605\) | |
304704.bz2 | 304704bz1 | \([0, 0, 0, -267996, 53585584]\) | \(-14647977776/59049\) | \(-8581111061004288\) | \([2]\) | \(2949120\) | \(1.9140\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 304704.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 304704.bz do not have complex multiplication.Modular form 304704.2.a.bz
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.