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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 6336.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6336.ba1 | 6336bv1 | \([0, 0, 0, -300, 592]\) | \(62500/33\) | \(1576599552\) | \([2]\) | \(2048\) | \(0.45644\) | \(\Gamma_0(N)\)-optimal |
6336.ba2 | 6336bv2 | \([0, 0, 0, 1140, 4624]\) | \(1714750/1089\) | \(-104055570432\) | \([2]\) | \(4096\) | \(0.80301\) |
Rank
sage: E.rank()
The elliptic curves in class 6336.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 6336.ba do not have complex multiplication.Modular form 6336.2.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.