Show commands:
SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 16800bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16800.w1 | 16800bh1 | \([0, -1, 0, -5258, 123012]\) | \(16079333824/2953125\) | \(2953125000000\) | \([2]\) | \(27648\) | \(1.1113\) | \(\Gamma_0(N)\)-optimal |
16800.w2 | 16800bh2 | \([0, -1, 0, 10367, 701137]\) | \(1925134784/4465125\) | \(-285768000000000\) | \([2]\) | \(55296\) | \(1.4579\) |
Rank
sage: E.rank()
The elliptic curves in class 16800bh have rank \(1\).
Complex multiplication
The elliptic curves in class 16800bh do not have complex multiplication.Modular form 16800.2.a.bh
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.