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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 22848.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22848.bz1 | 22848ct2 | \([0, 1, 0, -1073889, -425939553]\) | \(1044942448578893426/7759962920241\) | \(1017113859881828352\) | \([2]\) | \(540672\) | \(2.2859\) | |
| 22848.bz2 | 22848ct1 | \([0, 1, 0, -24129, -15063489]\) | \(-23707171994692/1480419781911\) | \(-97020790827319296\) | \([2]\) | \(270336\) | \(1.9393\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22848.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 22848.bz do not have complex multiplication.Modular form 22848.2.a.bz
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.
