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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 6720.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6720.bk1 | 6720bx3 | \([0, 1, 0, -7201, 232799]\) | \(157551496201/13125\) | \(3440640000\) | \([2]\) | \(8192\) | \(0.87376\) | |
| 6720.bk2 | 6720bx2 | \([0, 1, 0, -481, 2975]\) | \(47045881/11025\) | \(2890137600\) | \([2, 2]\) | \(4096\) | \(0.52719\) | |
| 6720.bk3 | 6720bx1 | \([0, 1, 0, -161, -801]\) | \(1771561/105\) | \(27525120\) | \([2]\) | \(2048\) | \(0.18061\) | \(\Gamma_0(N)\)-optimal |
| 6720.bk4 | 6720bx4 | \([0, 1, 0, 1119, 19935]\) | \(590589719/972405\) | \(-254910136320\) | \([2]\) | \(8192\) | \(0.87376\) |
Rank
sage: E.rank()
The elliptic curves in class 6720.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 6720.bk do not have complex multiplication.Modular form 6720.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
