# Properties

 Label 11424r Number of curves $4$ Conductor $11424$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 11424r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11424.s3 11424r1 $$[0, 1, 0, -82, -280]$$ $$964430272/127449$$ $$8156736$$ $$[2, 2]$$ $$1792$$ $$0.054141$$ $$\Gamma_0(N)$$-optimal
11424.s1 11424r2 $$[0, 1, 0, -1272, -17892]$$ $$444893916104/9639$$ $$4935168$$ $$[2]$$ $$3584$$ $$0.40071$$
11424.s2 11424r3 $$[0, 1, 0, -337, 2015]$$ $$1036433728/122451$$ $$501559296$$ $$[2]$$ $$3584$$ $$0.40071$$
11424.s4 11424r4 $$[0, 1, 0, 128, -1288]$$ $$449455096/1753941$$ $$-898017792$$ $$[2]$$ $$3584$$ $$0.40071$$

## Rank

sage: E.rank()

The elliptic curves in class 11424r have rank $$1$$.

## Complex multiplication

The elliptic curves in class 11424r do not have complex multiplication.

## Modular form 11424.2.a.r

sage: E.q_eigenform(10)

$$q + q^{3} + 2 q^{5} - q^{7} + q^{9} - 2 q^{13} + 2 q^{15} - q^{17} - 8 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.