# Properties

 Label 287490ba Number of curves $4$ Conductor $287490$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("287490.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 287490ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
287490.ba4 287490ba1 [1, 1, 0, -28777, -12779771] [2] 4552704 $$\Gamma_0(N)$$-optimal
287490.ba3 287490ba2 [1, 1, 0, -1014457, -391872299] [2, 2] 9105408
287490.ba2 287490ba3 [1, 1, 0, -1589437, 101805529] [2] 18210816
287490.ba1 287490ba4 [1, 1, 0, -16210357, -25127758319] [2] 18210816

## Rank

sage: E.rank()

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

## Modular form 287490.2.a.ba

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.