# Properties

 Label 48400.q Number of curves 2 Conductor 48400 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("48400.q1")

sage: E.isogeny_class()

## Elliptic curves in class 48400.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.q1 48400e2 [0, 1, 0, -654408, 198113188]  608256
48400.q2 48400e1 [0, 1, 0, 11092, 10442188]  304128 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 48400.2.a.q

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 