Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 146523.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
146523.l1 | 146523j2 | \([1, 0, 0, -15996445, -8243582764]\) | \(3885442650361/1996623837\) | \(232621522482400052470677\) | \([2]\) | \(27869184\) | \(3.1758\) | |
146523.l2 | 146523j1 | \([1, 0, 0, -12821780, -17656464489]\) | \(2000852317801/2094417\) | \(244015153092164986857\) | \([2]\) | \(13934592\) | \(2.8293\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 146523.l have rank \(0\).
Complex multiplication
The elliptic curves in class 146523.l do not have complex multiplication.Modular form 146523.2.a.l
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.