# Properties

 Label 150.c Number of curves $4$ Conductor $150$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 150.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
150.c1 150a4 $$[1, 0, 0, -828, 9072]$$ $$502270291349/1889568$$ $$236196000$$ $$$$ $$80$$ $$0.46602$$
150.c2 150a2 $$[1, 0, 0, -53, -153]$$ $$131872229/18$$ $$2250$$ $$$$ $$16$$ $$-0.33870$$
150.c3 150a3 $$[1, 0, 0, -28, 272]$$ $$-19465109/248832$$ $$-31104000$$ $$$$ $$40$$ $$0.11945$$
150.c4 150a1 $$[1, 0, 0, -3, -3]$$ $$-24389/12$$ $$-1500$$ $$$$ $$8$$ $$-0.68527$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 150.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 150.c do not have complex multiplication.

## Modular form150.2.a.c

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 