Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 217672.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
217672.j1 | 217672e2 | \([0, 0, 0, -165451, 25902630]\) | \(50668941906/1127\) | \(11140738545664\) | \([2]\) | \(552960\) | \(1.6184\) | |
217672.j2 | 217672e1 | \([0, 0, 0, -9971, 435006]\) | \(-22180932/3703\) | \(-18302641896448\) | \([2]\) | \(276480\) | \(1.2718\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 217672.j have rank \(1\).
Complex multiplication
The elliptic curves in class 217672.j do not have complex multiplication.Modular form 217672.2.a.j
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.