# Properties

 Label 29645.g Number of curves $3$ Conductor $29645$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 29645.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.g1 29645o3 $$[0, -1, 1, -778675, -276403667]$$ $$-250523582464/13671875$$ $$-2849524727779296875$$ $$[]$$ $$388800$$ $$2.2994$$
29645.g2 29645o1 $$[0, -1, 1, -7905, 302763]$$ $$-262144/35$$ $$-7294783303115$$ $$[]$$ $$43200$$ $$1.2008$$ $$\Gamma_0(N)$$-optimal
29645.g3 29645o2 $$[0, -1, 1, 51385, -782244]$$ $$71991296/42875$$ $$-8936109546315875$$ $$[]$$ $$129600$$ $$1.7501$$

## Rank

sage: E.rank()

The elliptic curves in class 29645.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 29645.g do not have complex multiplication.

## Modular form 29645.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{4} + q^{5} - 2q^{9} + 2q^{12} + 5q^{13} - q^{15} + 4q^{16} + 3q^{17} + 2q^{19} + O(q^{20})$$

## 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.