# Properties

 Label 6384p Number of curves $4$ Conductor $6384$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("p1")

E.isogeny_class()

## Elliptic curves in class 6384p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6384.bg3 6384p1 $$[0, 1, 0, -932, -11268]$$ $$350104249168/2793$$ $$715008$$ $$[2]$$ $$2560$$ $$0.29545$$ $$\Gamma_0(N)$$-optimal
6384.bg2 6384p2 $$[0, 1, 0, -952, -10780]$$ $$93280467172/7800849$$ $$7988069376$$ $$[2, 2]$$ $$5120$$ $$0.64202$$
6384.bg1 6384p3 $$[0, 1, 0, -3232, 57620]$$ $$1823652903746/328593657$$ $$672959809536$$ $$[2]$$ $$10240$$ $$0.98860$$
6384.bg4 6384p4 $$[0, 1, 0, 1008, -47628]$$ $$55251546334/517244049$$ $$-1059315812352$$ $$[4]$$ $$10240$$ $$0.98860$$

## Rank

sage: E.rank()

The elliptic curves in class 6384p have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6384p do not have complex multiplication.

## Modular form6384.2.a.p

sage: E.q_eigenform(10)

$$q + q^{3} + 2 q^{5} + q^{7} + q^{9} + 4 q^{11} - 6 q^{13} + 2 q^{15} + 2 q^{17} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.