# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.h1 23520bc4 $$[0, -1, 0, -691896, 221748696]$$ $$608119035935048/826875$$ $$49807880640000$$ $$[2]$$ $$147456$$ $$1.9025$$
23520.h2 23520bc3 $$[0, -1, 0, -109776, -9315900]$$ $$2428799546888/778248135$$ $$46878778795322880$$ $$[2]$$ $$147456$$ $$1.9025$$
23520.h3 23520bc1 $$[0, -1, 0, -43626, 3411360]$$ $$1219555693504/43758225$$ $$329479130433600$$ $$[2, 2]$$ $$73728$$ $$1.5559$$ $$\Gamma_0(N)$$-optimal
23520.h4 23520bc2 $$[0, -1, 0, 16399, 12018945]$$ $$1012048064/130203045$$ $$-62743584936775680$$ $$[2]$$ $$147456$$ $$1.9025$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 23520.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} - 2q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.