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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4650.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4650.x1 | 4650bd2 | \([1, 1, 1, -5461188, 4909955781]\) | \(1152829477932246539641/3188367360\) | \(49818240000000\) | \([2]\) | \(99840\) | \(2.2864\) | |
| 4650.x2 | 4650bd1 | \([1, 1, 1, -341188, 76675781]\) | \(-281115640967896441/468084326400\) | \(-7313817600000000\) | \([2]\) | \(49920\) | \(1.9399\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4650.x have rank \(1\).
Complex multiplication
The elliptic curves in class 4650.x do not have complex multiplication.Modular form 4650.2.a.x
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.
