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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 6720.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6720.be1 | 6720bt3 | \([0, -1, 0, -6945, -207423]\) | \(282678688658/18600435\) | \(2437996216320\) | \([2]\) | \(12288\) | \(1.1265\) | |
| 6720.be2 | 6720bt2 | \([0, -1, 0, -1345, 15457]\) | \(4108974916/893025\) | \(58525286400\) | \([2, 2]\) | \(6144\) | \(0.77990\) | |
| 6720.be3 | 6720bt1 | \([0, -1, 0, -1265, 17745]\) | \(13674725584/945\) | \(15482880\) | \([2]\) | \(3072\) | \(0.43333\) | \(\Gamma_0(N)\)-optimal |
| 6720.be4 | 6720bt4 | \([0, -1, 0, 2975, 90625]\) | \(22208984782/40516875\) | \(-5310627840000\) | \([4]\) | \(12288\) | \(1.1265\) |
Rank
sage: E.rank()
The elliptic curves in class 6720.be have rank \(0\).
Complex multiplication
The elliptic curves in class 6720.be do not have complex multiplication.Modular form 6720.2.a.be
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.
