# Properties

 Label 115920.cy Number of curves $2$ Conductor $115920$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cy1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.cy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.cy1 115920eb1 $$[0, 0, 0, -3387, 41834]$$ $$1439069689/579600$$ $$1730676326400$$ $$[2]$$ $$147456$$ $$1.0463$$ $$\Gamma_0(N)$$-optimal
115920.cy2 115920eb2 $$[0, 0, 0, 11013, 303914]$$ $$49471280711/41992020$$ $$-125387499847680$$ $$[2]$$ $$294912$$ $$1.3928$$

## Rank

sage: E.rank()

The elliptic curves in class 115920.cy have rank $$0$$.

## Complex multiplication

The elliptic curves in class 115920.cy do not have complex multiplication.

## Modular form 115920.2.a.cy

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} - 2q^{11} + 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.