# Properties

 Label 187590ct Number of curves $6$ Conductor $187590$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("187590.g1")

sage: E.isogeny_class()

## Elliptic curves in class 187590ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
187590.g5 187590ct1 [1, 1, 0, -142808, 71446848] [2] 3981312 $$\Gamma_0(N)$$-optimal
187590.g4 187590ct2 [1, 1, 0, -3603928, 2626445632] [2, 2] 7962624
187590.g1 187590ct3 [1, 1, 0, -57629848, 168367163008] [2] 15925248
187590.g3 187590ct4 [1, 1, 0, -4955928, 474872832] [2, 2] 15925248
187590.g6 187590ct5 [1, 1, 0, 19684272, 3811155912] [2] 31850496
187590.g2 187590ct6 [1, 1, 0, -51228128, -140535029448] [2] 31850496

## Rank

sage: E.rank()

The elliptic curves in class 187590ct have rank $$1$$.

## Modular form 187590.2.a.g

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.