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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 414400.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414400.ba1 | 414400ba1 | \([0, 1, 0, -14464833, -21138797537]\) | \(653723433587069/1455505408\) | \(745218768896000000000\) | \([2]\) | \(30105600\) | \(2.8875\) | \(\Gamma_0(N)\)-optimal |
414400.ba2 | 414400ba2 | \([0, 1, 0, -9344833, -36309357537]\) | \(-176265952176509/1010177608832\) | \(-517210935721984000000000\) | \([2]\) | \(60211200\) | \(3.2341\) |
Rank
sage: E.rank()
The elliptic curves in class 414400.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 414400.ba do not have complex multiplication.Modular form 414400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.