Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 10830.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10830.k1 | 10830l3 | \([1, 0, 1, -224189, 40779086]\) | \(26487576322129/44531250\) | \(2095011888281250\) | \([2]\) | \(92160\) | \(1.8351\) | |
| 10830.k2 | 10830l2 | \([1, 0, 1, -18419, 201242]\) | \(14688124849/8122500\) | \(382130168422500\) | \([2, 2]\) | \(46080\) | \(1.4886\) | |
| 10830.k3 | 10830l1 | \([1, 0, 1, -11199, -454334]\) | \(3301293169/22800\) | \(1072646086800\) | \([2]\) | \(23040\) | \(1.1420\) | \(\Gamma_0(N)\)-optimal |
| 10830.k4 | 10830l4 | \([1, 0, 1, 71831, 1609142]\) | \(871257511151/527800050\) | \(-24830818344094050\) | \([2]\) | \(92160\) | \(1.8351\) |
Rank
sage: E.rank()
The elliptic curves in class 10830.k have rank \(1\).
Complex multiplication
The elliptic curves in class 10830.k do not have complex multiplication.Modular form 10830.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
