Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 493680.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.q1 | 493680q2 | \([0, -1, 0, -222196, -375172004]\) | \(-2675089395664/132580078125\) | \(-60127666120500000000\) | \([]\) | \(14929920\) | \(2.4752\) | |
493680.q2 | 493680q1 | \([0, -1, 0, 24644, 13749100]\) | \(3649586096/182395125\) | \(-82719767050272000\) | \([]\) | \(4976640\) | \(1.9259\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 493680.q have rank \(1\).
Complex multiplication
The elliptic curves in class 493680.q do not have complex multiplication.Modular form 493680.2.a.q
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.