# Properties

 Label 287490q Number of curves $2$ Conductor $287490$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("287490.q1")

sage: E.isogeny_class()

## Elliptic curves in class 287490q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
287490.q2 287490q1 [1, 1, 0, -317011292, -36369933689904]  491692032 $$\Gamma_0(N)$$-optimal
287490.q1 287490q2 [1, 1, 0, -18510828892, -961303594075184]  983384064

## Rank

sage: E.rank()

The elliptic curves in class 287490q have rank $$1$$.

## Modular form 287490.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 2q^{11} - q^{12} - 4q^{13} + q^{14} - q^{15} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 