Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64400.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.f1 64400m2 \([0, 1, 0, -732408, -235452812]\) \(1357792998752738/38897700625\) \(1244726420000000000\) \([2]\) \(1179648\) \(2.2504\)  
64400.f2 64400m1 \([0, 1, 0, -107408, 8297188]\) \(8564808605476/3081640625\) \(49306250000000000\) \([2]\) \(589824\) \(1.9038\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 64400.f have rank \(0\).

Complex multiplication

The elliptic curves in class 64400.f do not have complex multiplication.

Modular form 64400.2.a.f

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - q^{7} + q^{9} + 6q^{11} - 4q^{13} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.