# Properties

 Label 274890.ew Number of curves 6 Conductor 274890 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("274890.ew1")

sage: E.isogeny_class()

## Elliptic curves in class 274890.ew

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
274890.ew1 274890ew5 [1, 0, 0, -14314861, 20842617935] [2] 18874368
274890.ew2 274890ew3 [1, 0, 0, -974611, 263948285] [2, 2] 9437184
274890.ew3 274890ew2 [1, 0, 0, -362111, -80644215] [2, 2] 4718592
274890.ew4 274890ew1 [1, 0, 0, -358191, -82542279] [2] 2359296 $$\Gamma_0(N)$$-optimal
274890.ew5 274890ew4 [1, 0, 0, 187669, -303744939] [2] 9437184
274890.ew6 274890ew6 [1, 0, 0, 2565639, 1741648635] [2] 18874368

## Rank

sage: E.rank()

The elliptic curves in class 274890.ew have rank $$0$$.

## Modular form 274890.2.a.ew

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 6q^{13} - q^{15} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.