# Properties

 Label 23520.f Number of curves $2$ Conductor $23520$ CM no Rank $0$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 23520.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.f1 23520c1 $$[0, -1, 0, -1486, -19424]$$ $$140608/15$$ $$38739462720$$ $$$$ $$17920$$ $$0.76604$$ $$\Gamma_0(N)$$-optimal
23520.f2 23520c2 $$[0, -1, 0, 1944, -99000]$$ $$39304/225$$ $$-4648735526400$$ $$$$ $$35840$$ $$1.1126$$

## Rank

sage: E.rank()

The elliptic curves in class 23520.f have rank $$0$$.

## Complex multiplication

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

## Modular form 23520.2.a.f

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} - 2q^{11} + 2q^{13} + q^{15} - 4q^{19} + O(q^{20})$$ ## 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. 