# Properties

 Label 23520.z Number of curves $4$ Conductor $23520$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.z1 23520bs4 $$[0, 1, 0, -54896, 4932360]$$ $$303735479048/105$$ $$6324810240$$ $$[2]$$ $$73728$$ $$1.2365$$
23520.z2 23520bs3 $$[0, 1, 0, -7121, -117825]$$ $$82881856/36015$$ $$17355279298560$$ $$[2]$$ $$73728$$ $$1.2365$$
23520.z3 23520bs1 $$[0, 1, 0, -3446, 75480]$$ $$601211584/11025$$ $$83013134400$$ $$[2, 2]$$ $$36864$$ $$0.88997$$ $$\Gamma_0(N)$$-optimal
23520.z4 23520bs2 $$[0, 1, 0, -16, 222284]$$ $$-8/354375$$ $$-21346234560000$$ $$[2]$$ $$73728$$ $$1.2365$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 23520.2.a.z

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.