Show commands:
SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 344760.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344760.bk1 | 344760bk2 | \([0, 1, 0, -101456, -10034400]\) | \(11683450802/2390625\) | \(23632056864000000\) | \([2]\) | \(2488320\) | \(1.8573\) | |
| 344760.bk2 | 344760bk1 | \([0, 1, 0, 13464, -932736]\) | \(54607676/108375\) | \(-535659955584000\) | \([2]\) | \(1244160\) | \(1.5107\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 344760.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 344760.bk do not have complex multiplication.Modular form 344760.2.a.bk
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.
