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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 64400.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64400.k1 | 64400bz2 | \([0, 1, 0, -10048008, 8910207988]\) | \(1753007192038126081/478174101507200\) | \(30603142496460800000000\) | \([2]\) | \(5160960\) | \(3.0224\) | |
64400.k2 | 64400bz1 | \([0, 1, 0, -3648008, -2571392012]\) | \(83890194895342081/3958384640000\) | \(253336616960000000000\) | \([2]\) | \(2580480\) | \(2.6758\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64400.k have rank \(0\).
Complex multiplication
The elliptic curves in class 64400.k do not have complex multiplication.Modular form 64400.2.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.