Show commands:
SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 272832ff
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 272832.ff2 | 272832ff1 | \([0, 1, 0, -3201, -24075297]\) | \(-117649/8118144\) | \(-250371512324849664\) | \([]\) | \(2032128\) | \(2.0174\) | \(\Gamma_0(N)\)-optimal |
| 272832.ff1 | 272832ff2 | \([0, 1, 0, -20418561, 35609947743]\) | \(-30526075007211889/103499257854\) | \(-3192018485186460647424\) | \([]\) | \(14224896\) | \(2.9903\) |
Rank
sage: E.rank()
The elliptic curves in class 272832ff have rank \(1\).
Complex multiplication
The elliptic curves in class 272832ff do not have complex multiplication.Modular form 272832.2.a.ff
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
