Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 152592w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152592.ct1 | 152592w1 | \([0, 1, 0, -4180192, -3264988300]\) | \(81706955619457/744505344\) | \(73607369161395142656\) | \([2]\) | \(7741440\) | \(2.6343\) | \(\Gamma_0(N)\)-optimal |
| 152592.ct2 | 152592w2 | \([0, 1, 0, -1220832, -7795176588]\) | \(-2035346265217/264305213568\) | \(-26131191109866849042432\) | \([2]\) | \(15482880\) | \(2.9809\) |
Rank
sage: E.rank()
The elliptic curves in class 152592w have rank \(1\).
Complex multiplication
The elliptic curves in class 152592w do not have complex multiplication.Modular form 152592.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
