# Properties

 Label 705600.cbu Number of curves $2$ Conductor $705600$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cbu1")

sage: E.isogeny_class()

## Elliptic curves in class 705600.cbu

sage: E.isogeny_class().curves

LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.cbu1 $$[0, 0, 0, -247327500, -1584025450000]$$ $$-7620530425/526848$$ $$-115675415850516480000000000$$ $$[]$$ $$238878720$$ $$3.7520$$
705600.cbu2 $$[0, 0, 0, 17272500, -2246650000]$$ $$2595575/1512$$ $$-331976639877120000000000$$ $$[]$$ $$79626240$$ $$3.2027$$

## Rank

sage: E.rank()

The elliptic curves in class 705600.cbu have rank $$1$$.

## Complex multiplication

The elliptic curves in class 705600.cbu do not have complex multiplication.

## Modular form 705600.2.a.cbu

sage: E.q_eigenform(10)

$$q + 6q^{11} + q^{13} - 3q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.