Properties

Label 64400.k
Number of curves $2$
Conductor $64400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: 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)
 
\(q - 2q^{3} + q^{7} + q^{9} + 2q^{11} + 4q^{13} + 2q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display

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.