# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ex1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.ex

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ex1 115920bu2 $$[0, 0, 0, -6627, -13246]$$ $$21558430658/12425175$$ $$18550686873600$$ $$[2]$$ $$229376$$ $$1.2355$$
115920.ex2 115920bu1 $$[0, 0, 0, 1653, -1654]$$ $$669136604/388815$$ $$-290248842240$$ $$[2]$$ $$114688$$ $$0.88895$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.ex

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} + 2 q^{11} - 4 q^{13} + 6 q^{17} - 8 q^{19} + O(q^{20})$$

## 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.