# Properties

 Label 2320f Number of curves $2$ Conductor $2320$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("f1")

E.isogeny_class()

## Elliptic curves in class 2320f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2320.e1 2320f1 $$[0, 0, 0, -43, -102]$$ $$2146689/145$$ $$593920$$ $$[2]$$ $$256$$ $$-0.14335$$ $$\Gamma_0(N)$$-optimal
2320.e2 2320f2 $$[0, 0, 0, 37, -438]$$ $$1367631/21025$$ $$-86118400$$ $$[2]$$ $$512$$ $$0.20322$$

## Rank

sage: E.rank()

The elliptic curves in class 2320f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2320f do not have complex multiplication.

## Modular form2320.2.a.f

sage: E.q_eigenform(10)

$$q - q^{5} + 2 q^{7} - 3 q^{9} + 6 q^{11} + 2 q^{13} - 2 q^{17} + 2 q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.