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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 43350k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43350.i2 | 43350k1 | \([1, 1, 0, -18786595, 16571903245]\) | \(247336189744145/103079215104\) | \(305598630754021225267200\) | \([]\) | \(9139200\) | \(3.2035\) | \(\Gamma_0(N)\)-optimal |
43350.i1 | 43350k2 | \([1, 1, 0, -5486759075, -156432971797875]\) | \(15773608170290225/31104\) | \(36021067485963750000000\) | \([]\) | \(45696000\) | \(4.0082\) |
Rank
sage: E.rank()
The elliptic curves in class 43350k have rank \(1\).
Complex multiplication
The elliptic curves in class 43350k do not have complex multiplication.Modular form 43350.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.