# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.k1 115920dd2 $$[0, 0, 0, -3617283, -1925328382]$$ $$1753007192038126081/478174101507200$$ $$1427820216314875084800$$ $$[2]$$ $$5160960$$ $$2.7670$$
115920.k2 115920dd1 $$[0, 0, 0, -1313283, 555158018]$$ $$83890194895342081/3958384640000$$ $$11819673200885760000$$ $$[2]$$ $$2580480$$ $$2.4204$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.k

sage: E.q_eigenform(10)

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

## 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.