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Properties

Label 63175r
Number of curves $2$
Conductor $63175$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 63175r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63175.d2 63175r1 \([0, -1, 1, 15042, 987318]\) \(4096/7\) \(-643205404296875\) \([]\) \(288000\) \(1.5264\) \(\Gamma_0(N)\)-optimal
63175.d1 63175r2 \([0, -1, 1, -1338708, -598723932]\) \(-2887553024/16807\) \(-1544336175716796875\) \([]\) \(1440000\) \(2.3311\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63175r have rank \(1\).

Complex multiplication

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

Modular form 63175.2.a.r

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.