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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 7200.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7200.ba1 | 7200bf2 | \([0, 0, 0, -36075, -2637250]\) | \(890277128/15\) | \(87480000000\) | \([2]\) | \(12288\) | \(1.2298\) | |
7200.ba2 | 7200bf3 | \([0, 0, 0, -9075, 292250]\) | \(14172488/1875\) | \(10935000000000\) | \([2]\) | \(12288\) | \(1.2298\) | |
7200.ba3 | 7200bf1 | \([0, 0, 0, -2325, -38500]\) | \(1906624/225\) | \(164025000000\) | \([2, 2]\) | \(6144\) | \(0.88325\) | \(\Gamma_0(N)\)-optimal |
7200.ba4 | 7200bf4 | \([0, 0, 0, 3300, -196000]\) | \(85184/405\) | \(-18895680000000\) | \([2]\) | \(12288\) | \(1.2298\) |
Rank
sage: E.rank()
The elliptic curves in class 7200.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 7200.ba do not have complex multiplication.Modular form 7200.2.a.ba
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.