# Properties

 Label 24150.bm Number of curves $2$ Conductor $24150$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bm1")

sage: E.isogeny_class()

## Elliptic curves in class 24150.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.bm1 24150bq1 $$[1, 1, 1, -588, 2781]$$ $$1439069689/579600$$ $$9056250000$$ $$$$ $$18432$$ $$0.60852$$ $$\Gamma_0(N)$$-optimal
24150.bm2 24150bq2 $$[1, 1, 1, 1912, 22781]$$ $$49471280711/41992020$$ $$-656125312500$$ $$$$ $$36864$$ $$0.95510$$

## Rank

sage: E.rank()

The elliptic curves in class 24150.bm have rank $$1$$.

## Complex multiplication

The elliptic curves in class 24150.bm do not have complex multiplication.

## Modular form 24150.2.a.bm

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} - 2q^{11} - q^{12} - 4q^{13} - q^{14} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 