# Properties

 Label 229320be Number of curves $4$ Conductor $229320$ CM no Rank $1$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("be1")

sage: E.isogeny_class()

## Elliptic curves in class 229320be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.q4 229320be1 $$[0, 0, 0, 4290342, 3717725893]$$ $$6364491337435136/8034291412875$$ $$-11025120151454371326000$$ $$[2]$$ $$17694720$$ $$2.9156$$ $$\Gamma_0(N)$$-optimal
229320.q3 229320be2 $$[0, 0, 0, -25893903, 35960536402]$$ $$87450143958975184/25164018140625$$ $$552504377521929924000000$$ $$[2, 2]$$ $$35389440$$ $$3.2621$$
229320.q1 229320be3 $$[0, 0, 0, -379849323, 2849127423478]$$ $$69014771940559650916/9797607421875$$ $$860470050462750000000000$$ $$[2]$$ $$70778880$$ $$3.6087$$
229320.q2 229320be4 $$[0, 0, 0, -154886403, -713666478098]$$ $$4678944235881273796/202428825314625$$ $$17778211968841718599296000$$ $$[2]$$ $$70778880$$ $$3.6087$$

## Rank

sage: E.rank()

The elliptic curves in class 229320be have rank $$1$$.

## Complex multiplication

The elliptic curves in class 229320be do not have complex multiplication.

## Modular form 229320.2.a.be

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{11} + q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.