# Properties

 Label 705600.z Number of curves $2$ Conductor $705600$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 705600.z

sage: E.isogeny_class().curves

LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.z1 $$[0, 0, 0, -9893100, 12672203600]$$ $$-7620530425/526848$$ $$-7403226614433054720000$$ $$[]$$ $$47775744$$ $$2.9473$$
705600.z2 $$[0, 0, 0, 690900, 17973200]$$ $$2595575/1512$$ $$-21246504952135680000$$ $$[]$$ $$15925248$$ $$2.3980$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 705600.2.a.z

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. 