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Properties

Label 63175y
Number of curves $2$
Conductor $63175$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 63175y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63175.x2 63175y1 \([0, 1, 1, 602, 8139]\) \(4096/7\) \(-41165145875\) \([]\) \(57600\) \(0.72169\) \(\Gamma_0(N)\)-optimal
63175.x1 63175y2 \([0, 1, 1, -53548, -4811211]\) \(-2887553024/16807\) \(-98837515245875\) \([]\) \(288000\) \(1.5264\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63175y have rank \(0\).

Complex multiplication

The elliptic curves in class 63175y do not have complex multiplication.

Modular form 63175.2.a.y

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{6} + q^{7} - 2 q^{9} - 3 q^{11} + 2 q^{12} + q^{13} + 2 q^{14} - 4 q^{16} - 7 q^{17} - 4 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.