Show commands:
SageMath
E = EllipticCurve("fw1")
E.isogeny_class()
Elliptic curves in class 457776.fw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 457776.fw1 | 457776fw1 | \([0, 0, 0, -8157603, -8962245470]\) | \(832972004929/610368\) | \(43991904225365065728\) | \([2]\) | \(21233664\) | \(2.7034\) | \(\Gamma_0(N)\)-optimal |
| 457776.fw2 | 457776fw2 | \([0, 0, 0, -6492963, -12725996510]\) | \(-420021471169/727634952\) | \(-52443848824663328980992\) | \([2]\) | \(42467328\) | \(3.0500\) |
Rank
sage: E.rank()
The elliptic curves in class 457776.fw have rank \(1\).
Complex multiplication
The elliptic curves in class 457776.fw do not have complex multiplication.Modular form 457776.2.a.fw
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
