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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 88200.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88200.bk1 | 88200cw2 | \([0, 0, 0, -22575, 1237250]\) | \(1272112/75\) | \(75014100000000\) | \([2]\) | \(294912\) | \(1.4156\) | |
| 88200.bk2 | 88200cw1 | \([0, 0, 0, 1050, 79625]\) | \(2048/45\) | \(-2813028750000\) | \([2]\) | \(147456\) | \(1.0691\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88200.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 88200.bk do not have complex multiplication.Modular form 88200.2.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.
