Show commands:
SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 22800.dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22800.dt1 | 22800dk4 | \([0, 1, 0, -1216008, -516528012]\) | \(3107086841064961/570\) | \(36480000000\) | \([2]\) | \(221184\) | \(1.8624\) | |
| 22800.dt2 | 22800dk3 | \([0, 1, 0, -88008, -5376012]\) | \(1177918188481/488703750\) | \(31277040000000000\) | \([2]\) | \(221184\) | \(1.8624\) | |
| 22800.dt3 | 22800dk2 | \([0, 1, 0, -76008, -8088012]\) | \(758800078561/324900\) | \(20793600000000\) | \([2, 2]\) | \(110592\) | \(1.5158\) | |
| 22800.dt4 | 22800dk1 | \([0, 1, 0, -4008, -168012]\) | \(-111284641/123120\) | \(-7879680000000\) | \([2]\) | \(55296\) | \(1.1692\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22800.dt have rank \(0\).
Complex multiplication
The elliptic curves in class 22800.dt do not have complex multiplication.Modular form 22800.2.a.dt
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
