# Properties

 Label 5184j Number of curves $2$ Conductor $5184$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("j1")

E.isogeny_class()

## Elliptic curves in class 5184j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5184.y1 5184j1 $$[0, 0, 0, -396, 3312]$$ $$-35937/4$$ $$-764411904$$ $$[]$$ $$2304$$ $$0.44191$$ $$\Gamma_0(N)$$-optimal
5184.y2 5184j2 $$[0, 0, 0, 2484, -4752]$$ $$109503/64$$ $$-990677827584$$ $$[]$$ $$6912$$ $$0.99122$$

## Rank

sage: E.rank()

The elliptic curves in class 5184j have rank $$1$$.

## Complex multiplication

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

## Modular form5184.2.a.j

sage: E.q_eigenform(10)

$$q + 3 q^{5} - 4 q^{7} + q^{13} - 3 q^{17} + 4 q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.