Show commands:
SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 118300.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
118300.bm1 | 118300y2 | \([0, -1, 0, -16618, -819963]\) | \(-262885120/343\) | \(-662238194800\) | \([]\) | \(233280\) | \(1.1753\) | |
118300.bm2 | 118300y1 | \([0, -1, 0, 282, -5383]\) | \(1280/7\) | \(-13515065200\) | \([]\) | \(77760\) | \(0.62599\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 118300.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 118300.bm do not have complex multiplication.Modular form 118300.2.a.bm
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.