# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("ba1")

E.isogeny_class()

## Elliptic curves in class 5184.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5184.ba1 5184r2 $$[0, 0, 0, -756, -7992]$$ $$790272$$ $$60466176$$ $$[]$$ $$1728$$ $$0.40153$$
5184.ba2 5184r1 $$[0, 0, 0, -36, 72]$$ $$6912$$ $$746496$$ $$[]$$ $$576$$ $$-0.14778$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5184.2.a.ba

sage: E.q_eigenform(10)

$$q + 3 q^{5} - q^{7} + 3 q^{11} + q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})$$

## 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 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.