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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 116886k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116886.s2 | 116886k1 | \([1, 0, 1, -469241, -123900856]\) | \(-6449916994998625/8532911772\) | \(-15116573711716092\) | \([2]\) | \(1290240\) | \(2.0110\) | \(\Gamma_0(N)\)-optimal |
116886.s1 | 116886k2 | \([1, 0, 1, -7510231, -7922501380]\) | \(26444015547214434625/46191222\) | \(81830567437542\) | \([2]\) | \(2580480\) | \(2.3575\) |
Rank
sage: E.rank()
The elliptic curves in class 116886k have rank \(1\).
Complex multiplication
The elliptic curves in class 116886k do not have complex multiplication.Modular form 116886.2.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 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.