# Properties

 Label 157170.x Number of curves $6$ Conductor $157170$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("157170.x1")

sage: E.isogeny_class()

## Elliptic curves in class 157170.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
157170.x1 157170cq6 [1, 0, 1, -51970884, -144211968938]  7864320
157170.x2 157170cq4 [1, 0, 1, -3248184, -2253510218] [2, 2] 3932160
157170.x3 157170cq5 [1, 0, 1, -3197484, -2327248298]  7864320
157170.x4 157170cq3 [1, 0, 1, -625304, 148334006]  3932160
157170.x5 157170cq2 [1, 0, 1, -206184, -34067018] [2, 2] 1966080
157170.x6 157170cq1 [1, 0, 1, 10136, -2224714]  983040 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 157170.x have rank $$1$$.

## Modular form 157170.2.a.x

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 