# Properties

 Label 69300.z Number of curves $4$ Conductor $69300$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 69300.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69300.z1 69300bj4 $$[0, 0, 0, -11159175, -7565103250]$$ $$52702650535889104/22020583921875$$ $$64212022716187500000000$$ $$$$ $$5971968$$ $$3.0734$$
69300.z2 69300bj2 $$[0, 0, 0, -9620175, -11484774250]$$ $$33766427105425744/9823275$$ $$28644669900000000$$ $$$$ $$1990656$$ $$2.5241$$
69300.z3 69300bj1 $$[0, 0, 0, -598800, -180991375]$$ $$-130287139815424/2250652635$$ $$-410181442728750000$$ $$$$ $$995328$$ $$2.1776$$ $$\Gamma_0(N)$$-optimal
69300.z4 69300bj3 $$[0, 0, 0, 2317200, -867344875]$$ $$7549996227362816/6152409907875$$ $$-1121276705710218750000$$ $$$$ $$2985984$$ $$2.7269$$

## Rank

sage: E.rank()

The elliptic curves in class 69300.z have rank $$0$$.

## Complex multiplication

The elliptic curves in class 69300.z do not have complex multiplication.

## Modular form 69300.2.a.z

sage: E.q_eigenform(10)

$$q - q^{7} + q^{11} - 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 