# Properties

 Label 48400k Number of curves 4 Conductor 48400 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("48400.cd1")

sage: E.isogeny_class()

## Elliptic curves in class 48400k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.cd3 48400k1 [0, 0, 0, -6050, 166375]  61440 $$\Gamma_0(N)$$-optimal
48400.cd2 48400k2 [0, 0, 0, -21175, -998250] [2, 2] 122880
48400.cd4 48400k3 [0, 0, 0, 39325, -5656750]  245760
48400.cd1 48400k4 [0, 0, 0, -323675, -70875750]  245760

## Rank

sage: E.rank()

The elliptic curves in class 48400k have rank $$0$$.

## Modular form 48400.2.a.cd

sage: E.q_eigenform(10)

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

## 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. 