# Properties

 Label 84150ga Number of curves $2$ Conductor $84150$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ga1")

sage: E.isogeny_class()

## Elliptic curves in class 84150ga

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
84150.gi2 84150ga1 [1, -1, 1, -2705, -43203] [2] 98304 $$\Gamma_0(N)$$-optimal
84150.gi1 84150ga2 [1, -1, 1, -40955, -3179703] [2] 196608

## Rank

sage: E.rank()

The elliptic curves in class 84150ga have rank $$1$$.

## Complex multiplication

The elliptic curves in class 84150ga do not have complex multiplication.

## Modular form 84150.2.a.ga

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2q^{7} + q^{8} + q^{11} - 4q^{13} + 2q^{14} + q^{16} + q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.