Show commands:
SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 28224.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28224.bz1 | 28224cj2 | \([0, 0, 0, -127596, 17479280]\) | \(238328\) | \(963961798754304\) | \([2]\) | \(172032\) | \(1.7298\) | |
28224.bz2 | 28224cj1 | \([0, 0, 0, -4116, 537824]\) | \(-64\) | \(-120495224844288\) | \([2]\) | \(86016\) | \(1.3832\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28224.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 28224.bz do not have complex multiplication.Modular form 28224.2.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.