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Properties

Label 64974.f
Number of curves $2$
Conductor $64974$
CM no
Rank $1$
Graph

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

Elliptic curves in class 64974.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64974.f1 64974e2 \([1, 1, 0, -23790, 1567644]\) \(-12657482097625/1813368648\) \(-213341008068552\) \([]\) \(269568\) \(1.4803\)  
64974.f2 64974e1 \([1, 1, 0, 1935, -5697]\) \(6804992375/4093362\) \(-481579945938\) \([]\) \(89856\) \(0.93096\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 64974.f have rank \(1\).

Complex multiplication

The elliptic curves in class 64974.f do not have complex multiplication.

Modular form 64974.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 6 q^{11} - q^{12} - q^{13} + q^{16} + q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.