# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("g1")

E.isogeny_class()

## Elliptic curves in class 5184.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5184.g1 5184l2 $$[0, 0, 0, -1404, -20304]$$ $$-316368$$ $$-967458816$$ $$[]$$ $$3456$$ $$0.59132$$
5184.g2 5184l1 $$[0, 0, 0, 36, -144]$$ $$432$$ $$-11943936$$ $$[]$$ $$1152$$ $$0.042015$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5184.2.a.g

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.