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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 145656.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145656.bk1 | 145656bp2 | \([0, 0, 0, -32079, 2210850]\) | \(21882096/7\) | \(1167872138496\) | \([2]\) | \(294912\) | \(1.2903\) | |
| 145656.bk2 | 145656bp1 | \([0, 0, 0, -1734, 44217]\) | \(-55296/49\) | \(-510944060592\) | \([2]\) | \(147456\) | \(0.94373\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145656.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 145656.bk do not have complex multiplication.Modular form 145656.2.a.bk
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.
