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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 6720.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6720.bx1 | 6720cb3 | \([0, 1, 0, -408240001, 3174701034815]\) | \(229625675762164624948320008/9568125\) | \(313528320000\) | \([2]\) | \(860160\) | \(3.1066\) | |
| 6720.bx2 | 6720cb2 | \([0, 1, 0, -25515001, 49598319815]\) | \(448487713888272974160064/91549016015625\) | \(374984769600000000\) | \([2, 2]\) | \(430080\) | \(2.7600\) | |
| 6720.bx3 | 6720cb4 | \([0, 1, 0, -25427521, 49955395679]\) | \(-55486311952875723077768/801237030029296875\) | \(-26254935000000000000000\) | \([2]\) | \(860160\) | \(3.1066\) | |
| 6720.bx4 | 6720cb1 | \([0, 1, 0, -1600156, 768989294]\) | \(7079962908642659949376/100085966990454375\) | \(6405501887389080000\) | \([2]\) | \(215040\) | \(2.4134\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6720.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 6720.bx do not have complex multiplication.Modular form 6720.2.a.bx
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.
