# Properties

 Label 23184.bh Number of curves $2$ Conductor $23184$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

## Elliptic curves in class 23184.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23184.bh1 23184p2 $$[0, 0, 0, -4395, 112138]$$ $$12576878500/1127$$ $$841300992$$ $$$$ $$15360$$ $$0.75255$$
23184.bh2 23184p1 $$[0, 0, 0, -255, 2014]$$ $$-9826000/3703$$ $$-691068672$$ $$$$ $$7680$$ $$0.40598$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 23184.bh have rank $$0$$.

## Complex multiplication

The elliptic curves in class 23184.bh do not have complex multiplication.

## Modular form 23184.2.a.bh

sage: E.q_eigenform(10)

$$q + q^{7} + 4q^{11} + 6q^{13} + O(q^{20})$$ ## 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. 