Properties

Label 64974w
Number of curves $2$
Conductor $64974$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 64974w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64974.y2 64974w1 \([1, 0, 1, 1469190, -3662344724]\) \(8691118430696801/148627738838592\) \(-5997665362391178001344\) \([2]\) \(4666368\) \(2.8593\) \(\Gamma_0(N)\)-optimal
64974.y1 64974w2 \([1, 0, 1, -28536450, -55296050036]\) \(63685588278222463519/4124615136744024\) \(166443098254419604094568\) \([2]\) \(9332736\) \(3.2059\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64974w have rank \(0\).

Complex multiplication

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

Modular form 64974.2.a.w

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