# Properties

 Label 23520.a Number of curves $2$ Conductor $23520$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.a1 23520bi1 $$[0, -1, 0, -67146, -6674604]$$ $$4446542056384/25725$$ $$193697313600$$ $$[2]$$ $$92160$$ $$1.3561$$ $$\Gamma_0(N)$$-optimal
23520.a2 23520bi2 $$[0, -1, 0, -65921, -6931119]$$ $$-65743598656/5294205$$ $$-2551226056888320$$ $$[2]$$ $$184320$$ $$1.7027$$

## Rank

sage: E.rank()

The elliptic curves in class 23520.a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 23520.a do not have complex multiplication.

## Modular form 23520.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} - 6q^{11} - 4q^{13} + q^{15} - 6q^{17} + 6q^{19} + O(q^{20})$$

## 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.