# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ep1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.ep

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ep1 115920er1 $$[0, 0, 0, -41386827, 64425512954]$$ $$2625564132023811051529/918925030195200000$$ $$2743895437362384076800000$$ $$[2]$$ $$13824000$$ $$3.3907$$ $$\Gamma_0(N)$$-optimal
115920.ep2 115920er2 $$[0, 0, 0, 123763893, 450316685306]$$ $$70213095586874240921591/69970703040000000000$$ $$-208931399746191360000000000$$ $$[2]$$ $$27648000$$ $$3.7373$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.ep

sage: E.q_eigenform(10)

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

## 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.