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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 121242ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121242.v2 | 121242ba1 | \([1, 1, 1, -4903, -173491]\) | \(-7357983625/2909808\) | \(-5154902370288\) | \([2]\) | \(215040\) | \(1.1482\) | \(\Gamma_0(N)\)-optimal |
121242.v1 | 121242ba2 | \([1, 1, 1, -84763, -9533083]\) | \(38017791015625/3681348\) | \(6521732544228\) | \([2]\) | \(430080\) | \(1.4948\) |
Rank
sage: E.rank()
The elliptic curves in class 121242ba have rank \(0\).
Complex multiplication
The elliptic curves in class 121242ba do not have complex multiplication.Modular form 121242.2.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 Cremona 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 Cremona labels.