# Properties

 Label 203280.eh Number of curves $4$ Conductor $203280$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("eh1")

sage: E.isogeny_class()

## Elliptic curves in class 203280.eh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.eh1 203280bz3 [0, 1, 0, -723136, 236447924] [2] 1966080
203280.eh2 203280bz2 [0, 1, 0, -45536, 3624564] [2, 2] 983040
203280.eh3 203280bz1 [0, 1, 0, -6816, -139020] [2] 491520 $$\Gamma_0(N)$$-optimal
203280.eh4 203280bz4 [0, 1, 0, 12544, 12290100] [2] 1966080

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 203280.2.a.eh

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.