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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 7920.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7920.bb1 | 7920bj3 | \([0, 0, 0, -599547, 136646314]\) | \(7981893677157049/1917731420550\) | \(5726315338059571200\) | \([2]\) | \(122880\) | \(2.3104\) | |
7920.bb2 | 7920bj2 | \([0, 0, 0, -203547, -33554486]\) | \(312341975961049/17862322500\) | \(53336609187840000\) | \([2, 2]\) | \(61440\) | \(1.9639\) | |
7920.bb3 | 7920bj1 | \([0, 0, 0, -200667, -34598774]\) | \(299270638153369/1069200\) | \(3192614092800\) | \([2]\) | \(30720\) | \(1.6173\) | \(\Gamma_0(N)\)-optimal |
7920.bb4 | 7920bj4 | \([0, 0, 0, 146373, -136920854]\) | \(116149984977671/2779502343750\) | \(-8299549526400000000\) | \([4]\) | \(122880\) | \(2.3104\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 7920.bb do not have complex multiplication.Modular form 7920.2.a.bb
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.