# Properties

 Label 287490.bc Number of curves $8$ Conductor $287490$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("287490.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 287490.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
287490.bc1 287490bc8 [1, 0, 1, -2629575229, -51901313272294] [2] 103809024
287490.bc2 287490bc6 [1, 0, 1, -164348479, -810968014594] [2, 2] 51904512
287490.bc3 287490bc7 [1, 0, 1, -163321729, -821600626894] [2] 103809024
287490.bc4 287490bc3 [1, 0, 1, -20630859, 36056522182] [2] 25952256
287490.bc5 287490bc4 [1, 0, 1, -10335979, -12505609594] [2, 2] 25952256
287490.bc6 287490bc2 [1, 0, 1, -1464859, 400095782] [2, 2] 12976128
287490.bc7 287490bc1 [1, 0, 1, 287461, 44725286] [2] 6488064 $$\Gamma_0(N)$$-optimal
287490.bc8 287490bc5 [1, 0, 1, 1738601, -39972864178] [2] 51904512

## Rank

sage: E.rank()

The elliptic curves in class 287490.bc have rank $$2$$.

## Modular form 287490.2.a.bc

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.