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SageMath
E = EllipticCurve("cbn1")
E.isogeny_class()
Elliptic curves in class 705600.cbn
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.cbn1 | \([0, 0, 0, -9893100, -12672203600]\) | \(-7620530425/526848\) | \(-7403226614433054720000\) | \([]\) | \(47775744\) | \(2.9473\) |
| 705600.cbn2 | \([0, 0, 0, 690900, -17973200]\) | \(2595575/1512\) | \(-21246504952135680000\) | \([]\) | \(15925248\) | \(2.3980\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.cbn have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.cbn do not have complex multiplication.Modular form 705600.2.a.cbn
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.
