Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 161448x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 161448.bg4 | 161448x1 | \([0, 1, 0, -7047, -1479762]\) | \(-2725888/64827\) | \(-920547218050992\) | \([2]\) | \(691200\) | \(1.5520\) | \(\Gamma_0(N)\)-optimal |
| 161448.bg3 | 161448x2 | \([0, 1, 0, -242492, -45837600]\) | \(6940769488/35721\) | \(8115844861184256\) | \([2, 2]\) | \(1382400\) | \(1.8986\) | |
| 161448.bg2 | 161448x3 | \([0, 1, 0, -377032, 10561568]\) | \(6522128932/3720087\) | \(3380829087887612928\) | \([2]\) | \(2764800\) | \(2.2452\) | |
| 161448.bg1 | 161448x4 | \([0, 1, 0, -3875072, -2937371280]\) | \(7080974546692/189\) | \(171763912406016\) | \([2]\) | \(2764800\) | \(2.2452\) |
Rank
sage: E.rank()
The elliptic curves in class 161448x have rank \(0\).
Complex multiplication
The elliptic curves in class 161448x do not have complex multiplication.Modular form 161448.2.a.x
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 Cremona 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 Cremona labels.
