# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("48400.w1")

sage: E.isogeny_class()

## Elliptic curves in class 48400.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.w1 48400cp4 [0, 1, 0, -21478508, -38320869512]  2488320
48400.w2 48400cp3 [0, 1, 0, -1347133, -594672762]  1244160
48400.w3 48400cp2 [0, 1, 0, -303508, -36469512]  829440
48400.w4 48400cp1 [0, 1, 0, -137133, 19099738]  414720 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 48400.2.a.w

sage: E.q_eigenform(10)

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

## 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. 