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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 84525.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84525.cb1 | 84525cf1 | \([0, 1, 1, -26133, -5038981]\) | \(-1073741824/5325075\) | \(-9788902323046875\) | \([]\) | \(497664\) | \(1.7528\) | \(\Gamma_0(N)\)-optimal |
| 84525.cb2 | 84525cf2 | \([0, 1, 1, 231117, 123200144]\) | \(742692847616/3992296875\) | \(-7338902110107421875\) | \([]\) | \(1492992\) | \(2.3021\) |
Rank
sage: E.rank()
The elliptic curves in class 84525.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 84525.cb do not have complex multiplication.Modular form 84525.2.a.cb
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
