# Properties

 Label 48400ck Number of curves 2 Conductor 48400 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("48400.s1")

sage: E.isogeny_class()

## Elliptic curves in class 48400ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.s2 48400ck1 [0, 1, 0, -128, -332] [] 13824 $$\Gamma_0(N)$$-optimal
48400.s1 48400ck2 [0, 1, 0, -8928, -327692] [] 41472

## Rank

sage: E.rank()

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

## Modular form 48400.2.a.s

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.