# Properties

 Label 1050p Number of curves $4$ Conductor $1050$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 1050p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.q3 1050p1 $$[1, 0, 0, -88, -208]$$ $$4826809/1680$$ $$26250000$$ $$[2]$$ $$384$$ $$0.12515$$ $$\Gamma_0(N)$$-optimal
1050.q2 1050p2 $$[1, 0, 0, -588, 5292]$$ $$1439069689/44100$$ $$689062500$$ $$[2, 2]$$ $$768$$ $$0.47173$$
1050.q1 1050p3 $$[1, 0, 0, -9338, 346542]$$ $$5763259856089/5670$$ $$88593750$$ $$[2]$$ $$1536$$ $$0.81830$$
1050.q4 1050p4 $$[1, 0, 0, 162, 18042]$$ $$30080231/9003750$$ $$-140683593750$$ $$[2]$$ $$1536$$ $$0.81830$$

## Rank

sage: E.rank()

The elliptic curves in class 1050p have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1050p do not have complex multiplication.

## Modular form1050.2.a.p

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.