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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 111090.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111090.k1 | 111090j2 | \([1, 1, 0, -104040062, 406861650804]\) | \(10236276715651320972447503/45003627643509964800\) | \(547559137538585741721600\) | \([2]\) | \(25804800\) | \(3.4076\) | |
111090.k2 | 111090j1 | \([1, 1, 0, -9832062, -851731596]\) | \(8639211347488146591503/4974033166663680000\) | \(60519061538796994560000\) | \([2]\) | \(12902400\) | \(3.0610\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 111090.k have rank \(1\).
Complex multiplication
The elliptic curves in class 111090.k do not have complex multiplication.Modular form 111090.2.a.k
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.