# Properties

 Label 287490.dl Number of curves $8$ Conductor $287490$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("287490.dl1")

sage: E.isogeny_class()

## Elliptic curves in class 287490.dl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
287490.dl1 287490dl8 [1, 0, 0, -480837321, -4058351458599] [2] 55738368
287490.dl2 287490dl6 [1, 0, 0, -30053001, -63410657895] [2, 2] 27869184
287490.dl3 287490dl7 [1, 0, 0, -27862601, -73045351335] [2] 55738368
287490.dl4 287490dl5 [1, 0, 0, -5965446, -5509954224] [2] 18579456
287490.dl5 287490dl3 [1, 0, 0, -2015881, -837413479] [2] 13934592
287490.dl6 287490dl2 [1, 0, 0, -790626, 141984180] [2, 2] 9289728
287490.dl7 287490dl1 [1, 0, 0, -681106, 216216836] [2] 4644864 $$\Gamma_0(N)$$-optimal
287490.dl8 287490dl4 [1, 0, 0, 2631874, 1043470680] [2] 18579456

## Rank

sage: E.rank()

The elliptic curves in class 287490.dl have rank $$0$$.

## Modular form 287490.2.a.dl

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.