# Properties

 Label 5184.z Number of curves $2$ Conductor $5184$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 5184.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5184.z1 5184y1 $$[0, 0, 0, -156, -752]$$ $$-316368$$ $$-1327104$$ $$[]$$ $$1152$$ $$0.042015$$ $$\Gamma_0(N)$$-optimal
5184.z2 5184y2 $$[0, 0, 0, 324, -3888]$$ $$432$$ $$-8707129344$$ $$[]$$ $$3456$$ $$0.59132$$

## Rank

sage: E.rank()

The elliptic curves in class 5184.z have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5184.z do not have complex multiplication.

## Modular form5184.2.a.z

sage: E.q_eigenform(10)

$$q + 3 q^{5} - 2 q^{7} + 6 q^{11} - 5 q^{13} + 3 q^{17} + 2 q^{19} + O(q^{20})$$

## 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.