# Properties

 Label 115920cs Number of curves $2$ Conductor $115920$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cs1")

sage: E.isogeny_class()

## Elliptic curves in class 115920cs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ee1 115920cs1 $$[0, 0, 0, -66387, 6417234]$$ $$292583028222603/8456021875$$ $$935168371200000$$ $$[2]$$ $$552960$$ $$1.6506$$ $$\Gamma_0(N)$$-optimal
115920.ee2 115920cs2 $$[0, 0, 0, 15933, 21284226]$$ $$4044759171237/1771943359375$$ $$-195962760000000000$$ $$[2]$$ $$1105920$$ $$1.9972$$

## Rank

sage: E.rank()

The elliptic curves in class 115920cs have rank $$1$$.

## Complex multiplication

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

## Modular form 115920.2.a.cs

sage: E.q_eigenform(10)

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

## 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.