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Properties

Label 63175l
Number of curves $2$
Conductor $63175$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 63175l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63175.c2 63175l1 \([0, -1, 1, -1898258, -5767937082]\) \(-1029077364736/18960396875\) \(-13937633985844091796875\) \([]\) \(5184000\) \(2.9301\) \(\Gamma_0(N)\)-optimal
63175.c1 63175l2 \([0, -1, 1, -150359508, 932115477918]\) \(-511416541770305536/214587319023035\) \(-157741398044792826075546875\) \([]\) \(25920000\) \(3.7349\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 63175.2.a.l

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