# Properties

 Label 6384.m Number of curves $4$ Conductor $6384$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 6384.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6384.m1 6384u4 $$[0, -1, 0, -19472, 1052352]$$ $$199350693197713/547428$$ $$2242265088$$ $$$$ $$6144$$ $$1.0274$$
6384.m2 6384u3 $$[0, -1, 0, -3472, -57152]$$ $$1130389181713/295568028$$ $$1210646642688$$ $$$$ $$6144$$ $$1.0274$$
6384.m3 6384u2 $$[0, -1, 0, -1232, 16320]$$ $$50529889873/2547216$$ $$10433396736$$ $$[2, 2]$$ $$3072$$ $$0.68083$$
6384.m4 6384u1 $$[0, -1, 0, 48, 960]$$ $$2924207/102144$$ $$-418381824$$ $$$$ $$1536$$ $$0.33426$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6384.m have rank $$1$$.

## Complex multiplication

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

## Modular form6384.2.a.m

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{5} + q^{7} + q^{9} + 2 q^{13} - 2 q^{15} - 2 q^{17} - q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 