# Properties

 Label 23520.d Number of curves $4$ Conductor $23520$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.d1 23520d4 $$[0, -1, 0, -33336, -2330460]$$ $$68017239368/39375$$ $$2371803840000$$ $$$$ $$49152$$ $$1.3201$$
23520.d2 23520d3 $$[0, -1, 0, -19616, 1048776]$$ $$13858588808/229635$$ $$13832359994880$$ $$$$ $$49152$$ $$1.3201$$
23520.d3 23520d1 $$[0, -1, 0, -2466, -21384]$$ $$220348864/99225$$ $$747118209600$$ $$[2, 2]$$ $$24576$$ $$0.97357$$ $$\Gamma_0(N)$$-optimal
23520.d4 23520d2 $$[0, -1, 0, 8559, -169119]$$ $$143877824/108045$$ $$-52065837895680$$ $$$$ $$49152$$ $$1.3201$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 23520.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} + q^{15} + 2q^{17} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 