Properties

Label 63175d
Number of curves $3$
Conductor $63175$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 63175d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63175.n2 63175d1 \([0, 1, 1, -12033, -567656]\) \(-262144/35\) \(-25728216171875\) \([]\) \(114048\) \(1.3058\) \(\Gamma_0(N)\)-optimal
63175.n3 63175d2 \([0, 1, 1, 78217, 1462969]\) \(71991296/42875\) \(-31517064810546875\) \([]\) \(342144\) \(1.8551\)  
63175.n1 63175d3 \([0, 1, 1, -1185283, 519182094]\) \(-250523582464/13671875\) \(-10050084442138671875\) \([]\) \(1026432\) \(2.4044\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 63175.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{4} - q^{7} - 2q^{9} - 3q^{11} - 2q^{12} + 5q^{13} + 4q^{16} - 3q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.