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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2070.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2070.k1 | 2070o2 | \([1, -1, 1, -28548518, 57983424981]\) | \(3529773792266261468365081/50841342773437500000\) | \(37063338881835937500000\) | \([2]\) | \(276480\) | \(3.1346\) | |
2070.k2 | 2070o1 | \([1, -1, 1, -204998, 2452800597]\) | \(-1306902141891515161/3564268498800000000\) | \(-2598351735625200000000\) | \([2]\) | \(138240\) | \(2.7880\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2070.k have rank \(0\).
Complex multiplication
The elliptic curves in class 2070.k do not have complex multiplication.Modular form 2070.2.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.