# Properties

 Label 203280.fx Number of curves $6$ Conductor $203280$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("203280.fx1")

sage: E.isogeny_class()

## Elliptic curves in class 203280.fx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.fx1 203280ff6 [0, 1, 0, -1268120, -550063692]  2621440
203280.fx2 203280ff4 [0, 1, 0, -82320, -7915932] [2, 2] 1310720
203280.fx3 203280ff2 [0, 1, 0, -21820, 1110668] [2, 2] 655360
203280.fx4 203280ff1 [0, 1, 0, -21215, 1182300]  327680 $$\Gamma_0(N)$$-optimal
203280.fx5 203280ff3 [0, 1, 0, 29000, 5562500]  1310720
203280.fx6 203280ff5 [0, 1, 0, 135480, -42502572]  2621440

## Rank

sage: E.rank()

The elliptic curves in class 203280.fx have rank $$0$$.

## Modular form 203280.2.a.fx

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - q^{7} + q^{9} + 2q^{13} + q^{15} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 