Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 215600.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215600.q1 | 215600x2 | \([0, 1, 0, -4596608, -3794715212]\) | \(1426487591593/2156\) | \(16233679616000000\) | \([2]\) | \(4718592\) | \(2.3785\) | |
| 215600.q2 | 215600x1 | \([0, 1, 0, -284608, -60523212]\) | \(-338608873/13552\) | \(-102040271872000000\) | \([2]\) | \(2359296\) | \(2.0319\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 215600.q have rank \(1\).
Complex multiplication
The elliptic curves in class 215600.q do not have complex multiplication.Modular form 215600.2.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.
