# Properties

 Label 115920.ek Number of curves $2$ Conductor $115920$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ek1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.ek

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ek1 115920bv1 $$[0, 0, 0, -9499647, 10855002814]$$ $$508017439289666674384/21234429931640625$$ $$3962854251562500000000$$ $$$$ $$6881280$$ $$2.9092$$ $$\Gamma_0(N)$$-optimal
115920.ek2 115920bv2 $$[0, 0, 0, 4562853, 40248440314]$$ $$14073614784514581404/945607964406328125$$ $$-705892562997466320000000$$ $$$$ $$13762560$$ $$3.2557$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.ek

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} - 2 q^{11} + 6 q^{17} + 4 q^{19} + O(q^{20})$$

## 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 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. 