# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("48400.n1")

sage: E.isogeny_class()

## Elliptic curves in class 48400.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.n1 48400cl2 [0, 1, 0, -1080328, 431836788] [] 456192
48400.n2 48400cl1 [0, 1, 0, -15528, 379828] [] 152064 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 48400.2.a.n

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 LMFDB 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 LMFDB labels. 