# Properties

 Label 235200.qt Number of curves $6$ Conductor $235200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.qt1")

sage: E.isogeny_class()

## Elliptic curves in class 235200.qt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.qt1 235200qt5 [0, 1, 0, -1317121633, 18398252484863] [2] 56623104
235200.qt2 235200qt3 [0, 1, 0, -82321633, 287440884863] [2, 2] 28311552
235200.qt3 235200qt6 [0, 1, 0, -76833633, 327420964863] [2] 56623104
235200.qt4 235200qt4 [0, 1, 0, -29009633, -56851147137] [2] 28311552
235200.qt5 235200qt2 [0, 1, 0, -5489633, 3853972863] [2, 2] 14155776
235200.qt6 235200qt1 [0, 1, 0, 782367, 373012863] [2] 7077888 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 235200.qt have rank $$1$$.

## Modular form 235200.2.a.qt

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 4q^{11} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.