Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 493680.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.u1 | 493680u1 | \([0, -1, 0, -3622901, 2732205885]\) | \(-724731558068224/24623341875\) | \(-178674696828587520000\) | \([]\) | \(14929920\) | \(2.6598\) | \(\Gamma_0(N)\)-optimal |
493680.u2 | 493680u2 | \([0, -1, 0, 17111659, 9628520541]\) | \(76363175346569216/49717529296875\) | \(-360765996723000000000000\) | \([]\) | \(44789760\) | \(3.2091\) |
Rank
sage: E.rank()
The elliptic curves in class 493680.u have rank \(1\).
Complex multiplication
The elliptic curves in class 493680.u do not have complex multiplication.Modular form 493680.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.