# Properties

 Label 29435c Number of curves $3$ Conductor $29435$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 29435c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29435.c2 29435c1 $$[0, -1, 1, -1121, 16407]$$ $$-262144/35$$ $$-20818816235$$ $$[]$$ $$16632$$ $$0.71250$$ $$\Gamma_0(N)$$-optimal
29435.c3 29435c2 $$[0, -1, 1, 7289, -43304]$$ $$71991296/42875$$ $$-25503049887875$$ $$[]$$ $$49896$$ $$1.2618$$
29435.c1 29435c3 $$[0, -1, 1, -110451, -14743143]$$ $$-250523582464/13671875$$ $$-8132350091796875$$ $$[]$$ $$149688$$ $$1.8111$$

## Rank

sage: E.rank()

The elliptic curves in class 29435c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 29435c do not have complex multiplication.

## Modular form 29435.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{4} - q^{5} + q^{7} - 2q^{9} + 3q^{11} + 2q^{12} + 5q^{13} + q^{15} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})$$

## 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 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.