Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 55440bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55440.h2 | 55440bv1 | \([0, 0, 0, -1203, -19598]\) | \(-1740992427/492800\) | \(-54499737600\) | \([2]\) | \(36864\) | \(0.77542\) | \(\Gamma_0(N)\)-optimal |
55440.h1 | 55440bv2 | \([0, 0, 0, -20403, -1121678]\) | \(8493409990827/474320\) | \(52455997440\) | \([2]\) | \(73728\) | \(1.1220\) |
Rank
sage: E.rank()
The elliptic curves in class 55440bv have rank \(0\).
Complex multiplication
The elliptic curves in class 55440bv do not have complex multiplication.Modular form 55440.2.a.bv
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.