# Properties

 Label 29575.k Number of curves $3$ Conductor $29575$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 29575.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29575.k1 29575h3 $$[0, -1, 1, -554883, -166240332]$$ $$-250523582464/13671875$$ $$-1031117645263671875$$ $$[]$$ $$295488$$ $$2.2147$$
29575.k2 29575h1 $$[0, -1, 1, -5633, 182418]$$ $$-262144/35$$ $$-2639661171875$$ $$[]$$ $$32832$$ $$1.1160$$ $$\Gamma_0(N)$$-optimal
29575.k3 29575h2 $$[0, -1, 1, 36617, -472457]$$ $$71991296/42875$$ $$-3233584935546875$$ $$[]$$ $$98496$$ $$1.6653$$

## Rank

sage: E.rank()

The elliptic curves in class 29575.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 29575.k do not have complex multiplication.

## Modular form 29575.2.a.k

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{4} + q^{7} - 2q^{9} + 3q^{11} + 2q^{12} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})$$

## 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.