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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 200900k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200900.l1 | 200900k1 | \([0, 1, 0, -1108, -15212]\) | \(-768208/41\) | \(-8036000000\) | \([]\) | \(124416\) | \(0.65953\) | \(\Gamma_0(N)\)-optimal |
200900.l2 | 200900k2 | \([0, 1, 0, 5892, -29212]\) | \(115393712/68921\) | \(-13508516000000\) | \([]\) | \(373248\) | \(1.2088\) |
Rank
sage: E.rank()
The elliptic curves in class 200900k have rank \(0\).
Complex multiplication
The elliptic curves in class 200900k do not have complex multiplication.Modular form 200900.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.