# Properties

 Label 2448.k Number of curves 4 Conductor 2448 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2448.k1")

sage: E.isogeny_class()

## Elliptic curves in class 2448.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2448.k1 2448q4 [0, 0, 0, -16275, -552238]  6912
2448.k2 2448q3 [0, 0, 0, -14835, -695374]  3456
2448.k3 2448q2 [0, 0, 0, -6195, 187634]  2304
2448.k4 2448q1 [0, 0, 0, -435, 2162]  1152 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2448.k have rank $$0$$.

## Modular form2448.2.a.k

sage: E.q_eigenform(10)

$$q + 4q^{7} + 6q^{11} + 2q^{13} + q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 