# Properties

 Label 24150bl Number of curves $4$ Conductor $24150$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

## Elliptic curves in class 24150bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.bo3 24150bl1 $$[1, 1, 1, -3178088, 2334258281]$$ $$-227196402372228188089/19338934824115200$$ $$-302170856626800000000$$ $$$$ $$1105920$$ $$2.6746$$ $$\Gamma_0(N)$$-optimal
24150.bo2 24150bl2 $$[1, 1, 1, -51846088, 143666130281]$$ $$986396822567235411402169/6336721794060000$$ $$99011278032187500000$$ $$$$ $$2211840$$ $$3.0212$$
24150.bo4 24150bl3 $$[1, 1, 1, 18841537, 94207781]$$ $$47342661265381757089751/27397579603968000000$$ $$-428087181312000000000000$$ $$$$ $$3317760$$ $$3.2239$$
24150.bo1 24150bl4 $$[1, 1, 1, -75366463, 659455781]$$ $$3029968325354577848895529/1753440696000000000000$$ $$27397510875000000000000000$$ $$$$ $$6635520$$ $$3.5705$$

## Rank

sage: E.rank()

The elliptic curves in class 24150bl have rank $$0$$.

## Complex multiplication

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

## Modular form 24150.2.a.bl

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 