# Properties

 Label 48400.l Number of curves 4 Conductor 48400 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("48400.l1")

sage: E.isogeny_class()

## Elliptic curves in class 48400.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.l1 48400cn3 [0, 1, 0, -125033, -17055062]  207360
48400.l2 48400cn4 [0, 1, 0, -109908, -21320312]  414720
48400.l3 48400cn1 [0, 1, 0, -4033, 66438]  69120 $$\Gamma_0(N)$$-optimal
48400.l4 48400cn2 [0, 1, 0, 11092, 459688]  138240

## Rank

sage: E.rank()

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

## Modular form 48400.2.a.l

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{7} + q^{9} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 