# Properties

 Label 274890.dt Number of curves 2 Conductor 274890 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("274890.dt1")

sage: E.isogeny_class()

## Elliptic curves in class 274890.dt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
274890.dt1 274890dt2 [1, 1, 1, -576241, -168509041] [2] 3870720
274890.dt2 274890dt1 [1, 1, 1, -43121, -1535857] [2] 1935360 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 274890.dt have rank $$1$$.

## Modular form 274890.2.a.dt

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.