# Properties

 Label 29040.v Number of curves $4$ Conductor $29040$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 29040.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29040.v1 29040ce4 $$[0, -1, 0, -30249556, -64026275300]$$ $$6749703004355978704/5671875$$ $$2572306572000000$$ $$[2]$$ $$829440$$ $$2.6925$$
29040.v2 29040ce3 $$[0, -1, 0, -1890181, -1000400300]$$ $$-26348629355659264/24169921875$$ $$-685095855468750000$$ $$[2]$$ $$414720$$ $$2.3459$$
29040.v3 29040ce2 $$[0, -1, 0, -381916, -83523284]$$ $$13584145739344/1195803675$$ $$542320423497388800$$ $$[2]$$ $$276480$$ $$2.1432$$
29040.v4 29040ce1 $$[0, -1, 0, 26459, -6095384]$$ $$72268906496/606436875$$ $$-17189438667390000$$ $$[2]$$ $$138240$$ $$1.7966$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 29040.v have rank $$1$$.

## Complex multiplication

The elliptic curves in class 29040.v do not have complex multiplication.

## Modular form 29040.2.a.v

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + 2q^{7} + q^{9} - 2q^{13} + q^{15} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.