# Properties

 Label 203280cm Number of curves $6$ Conductor $203280$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cm1")

sage: E.isogeny_class()

## Elliptic curves in class 203280cm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.dk6 203280cm1 [0, -1, 0, 67720, -1970406480] [2] 7372800 $$\Gamma_0(N)$$-optimal
203280.dk5 203280cm2 [0, -1, 0, -23173960, -42169216208] [2, 2] 14745600
203280.dk4 203280cm3 [0, -1, 0, -49261560, 70195294512] [2] 29491200
203280.dk2 203280cm4 [0, -1, 0, -368953240, -2727629416400] [2, 2] 29491200
203280.dk3 203280cm5 [0, -1, 0, -367123720, -2756020639568] [2] 58982400
203280.dk1 203280cm6 [0, -1, 0, -5903251240, -174574223474000] [2] 58982400

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 203280cm do not have complex multiplication.

## Modular form 203280.2.a.cm

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.