# Properties

 Label 23520.o Number of curves $4$ Conductor $23520$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.o1 23520j4 $$[0, -1, 0, -3213240, 2217954600]$$ $$60910917333827912/3255076125$$ $$196073702927424000$$ $$[2]$$ $$442368$$ $$2.3855$$
23520.o2 23520j3 $$[0, -1, 0, -1038865, -379651775]$$ $$257307998572864/19456203375$$ $$9375755759064576000$$ $$[2]$$ $$442368$$ $$2.3855$$
23520.o3 23520j1 $$[0, -1, 0, -211990, 30643600]$$ $$139927692143296/27348890625$$ $$205924456521000000$$ $$[2, 2]$$ $$221184$$ $$2.0389$$ $$\Gamma_0(N)$$-optimal
23520.o4 23520j2 $$[0, -1, 0, 436280, 180782932]$$ $$152461584507448/322998046875$$ $$-19456203375000000000$$ $$[2]$$ $$442368$$ $$2.3855$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 23520.2.a.o

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.