Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 54208.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54208.u1 | 54208t2 | \([0, 1, 0, -19521, 1030687]\) | \(3543122/49\) | \(11377900126208\) | \([2]\) | \(184320\) | \(1.3109\) | |
54208.u2 | 54208t1 | \([0, 1, 0, -161, 43327]\) | \(-4/7\) | \(-812707151872\) | \([2]\) | \(92160\) | \(0.96428\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54208.u have rank \(0\).
Complex multiplication
The elliptic curves in class 54208.u do not have complex multiplication.Modular form 54208.2.a.u
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.