Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 286110.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286110.q1 | 286110q2 | \([1, -1, 0, -36936855, -86040178749]\) | \(64466729992673/306281250\) | \(26478186182244803531250\) | \([2]\) | \(26738688\) | \(3.1518\) | |
| 286110.q2 | 286110q1 | \([1, -1, 0, -1121085, -2725534575]\) | \(-1802485313/36085500\) | \(-3119611753835387761500\) | \([2]\) | \(13369344\) | \(2.8053\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286110.q have rank \(1\).
Complex multiplication
The elliptic curves in class 286110.q do not have complex multiplication.Modular form 286110.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
