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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 6720.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6720.bo1 | 6720v3 | \([0, 1, 0, -2721, -55521]\) | \(68017239368/39375\) | \(1290240000\) | \([2]\) | \(4096\) | \(0.69376\) | |
| 6720.bo2 | 6720v4 | \([0, 1, 0, -1601, 23775]\) | \(13858588808/229635\) | \(7524679680\) | \([2]\) | \(4096\) | \(0.69376\) | |
| 6720.bo3 | 6720v2 | \([0, 1, 0, -201, -585]\) | \(220348864/99225\) | \(406425600\) | \([2, 2]\) | \(2048\) | \(0.34719\) | |
| 6720.bo4 | 6720v1 | \([0, 1, 0, 44, -46]\) | \(143877824/108045\) | \(-6914880\) | \([2]\) | \(1024\) | \(0.00061629\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6720.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 6720.bo do not have complex multiplication.Modular form 6720.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
