# Properties

 Label 1050.i Number of curves $6$ Conductor $1050$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 1050.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.i1 1050h4 $$[1, 0, 1, -33601, 2367848]$$ $$268498407453697/252$$ $$3937500$$ $$[2]$$ $$2048$$ $$0.99382$$
1050.i2 1050h5 $$[1, 0, 1, -22851, -1318652]$$ $$84448510979617/933897762$$ $$14592152531250$$ $$[2]$$ $$4096$$ $$1.3404$$
1050.i3 1050h3 $$[1, 0, 1, -2601, 17848]$$ $$124475734657/63011844$$ $$984560062500$$ $$[2, 2]$$ $$2048$$ $$0.99382$$
1050.i4 1050h2 $$[1, 0, 1, -2101, 36848]$$ $$65597103937/63504$$ $$992250000$$ $$[2, 2]$$ $$1024$$ $$0.64725$$
1050.i5 1050h1 $$[1, 0, 1, -101, 848]$$ $$-7189057/16128$$ $$-252000000$$ $$[2]$$ $$512$$ $$0.30067$$ $$\Gamma_0(N)$$-optimal
1050.i6 1050h6 $$[1, 0, 1, 9649, 140348]$$ $$6359387729183/4218578658$$ $$-65915291531250$$ $$[2]$$ $$4096$$ $$1.3404$$

## Rank

sage: E.rank()

The elliptic curves in class 1050.i have rank $$1$$.

## Complex multiplication

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

## Modular form1050.2.a.i

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.