# Properties

 Label 203280.gb Number of curves $6$ Conductor $203280$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("203280.gb1")

sage: E.isogeny_class()

## Elliptic curves in class 203280.gb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.gb1 203280x6 [0, 1, 0, -25652040, -50013175500]  15728640
203280.gb2 203280x4 [0, 1, 0, -1694040, -688445100] [2, 2] 7864320
203280.gb3 203280x2 [0, 1, 0, -522760, 135667508] [2, 2] 3932160
203280.gb4 203280x1 [0, 1, 0, -513080, 141285780]  1966080 $$\Gamma_0(N)$$-optimal
203280.gb5 203280x3 [0, 1, 0, 493640, 600365588]  7864320
203280.gb6 203280x5 [0, 1, 0, 3523480, -4088181132]  15728640

## Rank

sage: E.rank()

The elliptic curves in class 203280.gb have rank $$1$$.

## Modular form 203280.2.a.gb

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - q^{7} + q^{9} + 2q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 