Show commands:
SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 36300.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36300.bz1 | 36300cg2 | \([0, 1, 0, -3670333, 2705266463]\) | \(-30866268160/3\) | \(-531468300000000\) | \([]\) | \(583200\) | \(2.2589\) | |
36300.bz2 | 36300cg1 | \([0, 1, 0, -40333, 4546463]\) | \(-40960/27\) | \(-4783214700000000\) | \([]\) | \(194400\) | \(1.7096\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36300.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 36300.bz do not have complex multiplication.Modular form 36300.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.