# Properties

 Label 48400cg Number of curves $2$ Conductor $48400$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cg1")

sage: E.isogeny_class()

## Elliptic curves in class 48400cg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.dh2 48400cg1 [0, -1, 0, -12008, 510512] [] 53760 $$\Gamma_0(N)$$-optimal
48400.dh1 48400cg2 [0, -1, 0, -122008, -64081488] [] 591360

## Rank

sage: E.rank()

The elliptic curves in class 48400cg have rank $$1$$.

## Complex multiplication

The elliptic curves in class 48400cg do not have complex multiplication.

## Modular form 48400.2.a.cg

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 