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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 26450.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26450.ba1 | 26450r2 | \([1, 1, 1, -1540988, 735644701]\) | \(109348914285625/1472\) | \(5447720715200\) | \([]\) | \(228096\) | \(2.0008\) | |
26450.ba2 | 26450r1 | \([1, 1, 1, -20113, 879571]\) | \(243135625/48668\) | \(180115266146300\) | \([]\) | \(76032\) | \(1.4515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26450.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 26450.ba do not have complex multiplication.Modular form 26450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.