Properties

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

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 64974.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64974.bw1 64974bx2 \([1, 0, 0, -87674406, 422770263012]\) \(-1521059241134755603512440881/695595284594977727840256\) \(-34084168945153908664172544\) \([7]\) \(14620032\) \(3.6057\)  
64974.bw2 64974bx1 \([1, 0, 0, -2226316, -1477144936]\) \(-24905087205614147556241/4819348696095929736\) \(-236148086108700557064\) \([]\) \(2088576\) \(2.6328\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 64974.2.a.bw

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} - 2 q^{11} + q^{12} - q^{13} - q^{15} + q^{16} + q^{17} + q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.