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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 5390.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5390.ba1 | 5390z2 | \([1, -1, 1, -15028, -703713]\) | \(9300746727/24200\) | \(976557289400\) | \([2]\) | \(10752\) | \(1.1762\) | |
5390.ba2 | 5390z1 | \([1, -1, 1, -1308, -1249]\) | \(6128487/3520\) | \(142044696640\) | \([2]\) | \(5376\) | \(0.82959\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5390.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 5390.ba do not have complex multiplication.Modular form 5390.2.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.