# Properties

 Label 203280j Number of curves $6$ Conductor $203280$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("203280.hb1")

sage: E.isogeny_class()

## Elliptic curves in class 203280j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.hb6 203280j1 [0, 1, 0, 19320, -1440012] [2] 983040 $$\Gamma_0(N)$$-optimal
203280.hb5 203280j2 [0, 1, 0, -135560, -15007500] [2, 2] 1966080
203280.hb4 203280j3 [0, 1, 0, -716360, 220332660] [2] 3932160
203280.hb2 203280j4 [0, 1, 0, -2032840, -1116188812] [2, 2] 3932160
203280.hb3 203280j5 [0, 1, 0, -1897320, -1271277900] [2] 7864320
203280.hb1 203280j6 [0, 1, 0, -32524840, -71406347212] [2] 7864320

## Rank

sage: E.rank()

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

## Modular form 203280.2.a.hb

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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.