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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 101150ck
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101150.cu2 | 101150ck1 | \([1, 1, 1, 227437, -8004719]\) | \(3449795831/2071552\) | \(-781284833392000000\) | \([2]\) | \(1843200\) | \(2.1226\) | \(\Gamma_0(N)\)-optimal |
101150.cu1 | 101150ck2 | \([1, 1, 1, -928563, -65804719]\) | \(234770924809/130960928\) | \(49391850561000500000\) | \([2]\) | \(3686400\) | \(2.4692\) |
Rank
sage: E.rank()
The elliptic curves in class 101150ck have rank \(1\).
Complex multiplication
The elliptic curves in class 101150ck do not have complex multiplication.Modular form 101150.2.a.ck
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.