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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 12600.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12600.bo1 | 12600bl2 | \([0, 0, 0, -2775, 56250]\) | \(21882096/7\) | \(756000000\) | \([2]\) | \(8192\) | \(0.67842\) | |
| 12600.bo2 | 12600bl1 | \([0, 0, 0, -150, 1125]\) | \(-55296/49\) | \(-330750000\) | \([2]\) | \(4096\) | \(0.33185\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12600.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 12600.bo do not have complex multiplication.Modular form 12600.2.a.bo
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.
