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Properties

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

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 64974.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64974.bl1 64974bd2 \([1, 1, 1, -4296045895, -145014496259011]\) \(-1521059241134755603512440881/695595284594977727840256\) \(-4009968392228412200431235629056\) \([]\) \(102340224\) \(4.5787\)  
64974.bl2 64974bd1 \([1, 1, 1, -109089485, 506551623563]\) \(-24905087205614147556241/4819348696095929736\) \(-27782586182602511838022536\) \([]\) \(14620032\) \(3.6057\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 64974.2.a.bl

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.