Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 88200.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88200.t1 | 88200cv4 | \([0, 0, 0, -19143075, 30349754750]\) | \(282678688658/18600435\) | \(51049189083604320000000\) | \([2]\) | \(7077888\) | \(3.1069\) | |
| 88200.t2 | 88200cv2 | \([0, 0, 0, -3708075, -2171790250]\) | \(4108974916/893025\) | \(1225460643296400000000\) | \([2, 2]\) | \(3538944\) | \(2.7603\) | |
| 88200.t3 | 88200cv1 | \([0, 0, 0, -3487575, -2506729750]\) | \(13674725584/945\) | \(324195937380000000\) | \([2]\) | \(1769472\) | \(2.4137\) | \(\Gamma_0(N)\)-optimal |
| 88200.t4 | 88200cv3 | \([0, 0, 0, 8198925, -13257207250]\) | \(22208984782/40516875\) | \(-111199206521340000000000\) | \([2]\) | \(7077888\) | \(3.1069\) |
Rank
sage: E.rank()
The elliptic curves in class 88200.t have rank \(1\).
Complex multiplication
The elliptic curves in class 88200.t do not have complex multiplication.Modular form 88200.2.a.t
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.
