Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 248256w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 248256.w2 | 248256w1 | \([0, 0, 0, -5196, 759440]\) | \(-81182737/1256796\) | \(-240177455824896\) | \([2]\) | \(516096\) | \(1.4407\) | \(\Gamma_0(N)\)-optimal |
| 248256.w1 | 248256w2 | \([0, 0, 0, -160716, 24709520]\) | \(2402335209457/10031094\) | \(1916971915935744\) | \([2]\) | \(1032192\) | \(1.7873\) |
Rank
sage: E.rank()
The elliptic curves in class 248256w have rank \(0\).
Complex multiplication
The elliptic curves in class 248256w do not have complex multiplication.Modular form 248256.2.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.
