# Properties

 Label 17136y Number of curves $6$ Conductor $17136$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("17136.bg1")

sage: E.isogeny_class()

## Elliptic curves in class 17136y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17136.bg5 17136y1 [0, 0, 0, -10115139, 12366939202] [2] 737280 $$\Gamma_0(N)$$-optimal
17136.bg4 17136y2 [0, 0, 0, -13064259, 4567696450] [2, 2] 1474560
17136.bg2 17136y3 [0, 0, 0, -123702339, -525941897150] [2, 2] 2949120
17136.bg6 17136y4 [0, 0, 0, 50387901, 35925753922] [2] 2949120
17136.bg1 17136y5 [0, 0, 0, -1975478979, -33795331366718] [2] 5898240
17136.bg3 17136y6 [0, 0, 0, -42134979, -1209166417982] [2] 5898240

## Rank

sage: E.rank()

The elliptic curves in class 17136y have rank $$1$$.

## Modular form 17136.2.a.bg

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{7} + 4q^{11} - 2q^{13} - q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.