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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 81225.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81225.ba1 | 81225q2 | \([0, 0, 1, -23663550, 32991575656]\) | \(7575076864/1953125\) | \(377838667507598876953125\) | \([]\) | \(8273664\) | \(3.2333\) | |
| 81225.ba2 | 81225q1 | \([0, 0, 1, -8230800, -9085817219]\) | \(318767104/125\) | \(24181674720486328125\) | \([]\) | \(2757888\) | \(2.6840\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 81225.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 81225.ba do not have complex multiplication.Modular form 81225.2.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.
