# Properties

 Label 115920.et Number of curves $4$ Conductor $115920$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("et1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.et

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.et1 115920bt4 $$[0, 0, 0, -30987, 2099466]$$ $$4407931365156/100625$$ $$75116160000$$ $$[2]$$ $$163840$$ $$1.2004$$
115920.et2 115920bt3 $$[0, 0, 0, -8307, -260766]$$ $$84923690436/9794435$$ $$7311506549760$$ $$[2]$$ $$163840$$ $$1.2004$$
115920.et3 115920bt2 $$[0, 0, 0, -2007, 30294]$$ $$4790692944/648025$$ $$120937017600$$ $$[2, 2]$$ $$81920$$ $$0.85380$$
115920.et4 115920bt1 $$[0, 0, 0, 198, 2511]$$ $$73598976/276115$$ $$-3220605360$$ $$[2]$$ $$40960$$ $$0.50723$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.et

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.