# Properties

 Label 1122b Number of curves $4$ Conductor $1122$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 1122b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.c3 1122b1 $$[1, 1, 0, -8279, -264363]$$ $$62768149033310713/6915442583808$$ $$6915442583808$$ $$[2]$$ $$3840$$ $$1.1971$$ $$\Gamma_0(N)$$-optimal
1122.c2 1122b2 $$[1, 1, 0, -31399, 1848805]$$ $$3423676911662954233/483711578981136$$ $$483711578981136$$ $$[2, 2]$$ $$7680$$ $$1.5437$$
1122.c1 1122b3 $$[1, 1, 0, -483939, 129374577]$$ $$12534210458299016895673/315581882565708$$ $$315581882565708$$ $$[2]$$ $$15360$$ $$1.8903$$
1122.c4 1122b4 $$[1, 1, 0, 51221, 10028185]$$ $$14861225463775641287/51859390496937804$$ $$-51859390496937804$$ $$[2]$$ $$15360$$ $$1.8903$$

## Rank

sage: E.rank()

The elliptic curves in class 1122b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1122b do not have complex multiplication.

## Modular form1122.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9} - 2 q^{10} + q^{11} - q^{12} + 6 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} - q^{17} - q^{18} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.