# Properties

 Label 48400.r Number of curves 2 Conductor 48400 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("48400.r1")

sage: E.isogeny_class()

## Elliptic curves in class 48400.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.r1 48400de2 [0, 1, 0, -5107208, 4438969588]  1382400
48400.r2 48400de1 [0, 1, 0, -267208, 92649588]  691200 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 48400.2.a.r

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 