# Properties

 Label 369600uq Number of curves $4$ Conductor $369600$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("uq1")

sage: E.isogeny_class()

## Elliptic curves in class 369600uq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.uq3 369600uq1 $$[0, 1, 0, -58697233, 173071463663]$$ $$87364831012240243408/1760913$$ $$450793728000000$$ $$[2]$$ $$23592960$$ $$2.7953$$ $$\Gamma_0(N)$$-optimal
369600.uq2 369600uq2 $$[0, 1, 0, -58699233, 173059077663]$$ $$21843440425782779332/3100814593569$$ $$3175234143814656000000$$ $$[2, 2]$$ $$47185920$$ $$3.1419$$
369600.uq4 369600uq3 $$[0, 1, 0, -53407233, 205536081663]$$ $$-8226100326647904626/4152140742401883$$ $$-8503584240439056384000000$$ $$[2]$$ $$94371840$$ $$3.4884$$
369600.uq1 369600uq4 $$[0, 1, 0, -64023233, 139789401663]$$ $$14171198121996897746/4077720290568771$$ $$8351171155084843008000000$$ $$[2]$$ $$94371840$$ $$3.4884$$

## Rank

sage: E.rank()

The elliptic curves in class 369600uq have rank $$1$$.

## Complex multiplication

The elliptic curves in class 369600uq do not have complex multiplication.

## Modular form 369600.2.a.uq

sage: E.q_eigenform(10)

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

## 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.