# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 63175.n

sage: E.isogeny_class().curves

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

## Rank

sage: E.rank()

The elliptic curves in class 63175.n have rank $$0$$.

## Complex multiplication

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

## Modular form 63175.2.a.n

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} - q^{7} - 2q^{9} - 3q^{11} - 2q^{12} + 5q^{13} + 4q^{16} - 3q^{17} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.