Show commands:
SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 201840.cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 201840.cv1 | 201840a3 | \([0, 1, 0, -3465200, 2445222420]\) | \(1888690601881/31827645\) | \(77544757241893048320\) | \([2]\) | \(10321920\) | \(2.6144\) | |
| 201840.cv2 | 201840a2 | \([0, 1, 0, -437600, -53153100]\) | \(3803721481/1703025\) | \(4149243847663718400\) | \([2, 2]\) | \(5160960\) | \(2.2679\) | |
| 201840.cv3 | 201840a1 | \([0, 1, 0, -370320, -86820012]\) | \(2305199161/1305\) | \(3179497201274880\) | \([2]\) | \(2580480\) | \(1.9213\) | \(\Gamma_0(N)\)-optimal |
| 201840.cv4 | 201840a4 | \([0, 1, 0, 1513520, -395769772]\) | \(157376536199/118918125\) | \(-289731682466173440000\) | \([4]\) | \(10321920\) | \(2.6144\) |
Rank
sage: E.rank()
The elliptic curves in class 201840.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 201840.cv do not have complex multiplication.Modular form 201840.2.a.cv
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.
