# Properties

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

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("es1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.es

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.es1 115920es4 $$[0, 0, 0, -62320467, 189362579474]$$ $$8964546681033941529169/31696875000$$ $$94646361600000000$$ $$[2]$$ $$7077888$$ $$2.8997$$
115920.es2 115920es3 $$[0, 0, 0, -5192787, 820437266]$$ $$5186062692284555089/2903809817953800$$ $$8670729655452959539200$$ $$[2]$$ $$7077888$$ $$2.8997$$
115920.es3 115920es2 $$[0, 0, 0, -3896787, 2955986066]$$ $$2191574502231419089/4115217960000$$ $$12287974985072640000$$ $$[2, 2]$$ $$3538944$$ $$2.5532$$
115920.es4 115920es1 $$[0, 0, 0, -164307, 76750994]$$ $$-164287467238609/757170892800$$ $$-2260900171166515200$$ $$[2]$$ $$1769472$$ $$2.2066$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.es

sage: E.q_eigenform(10)

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

## 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.