# Properties

 Label 323400.ct Number of curves $2$ Conductor $323400$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

## Elliptic curves in class 323400.ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
323400.ct1 323400ct2 $$[0, -1, 0, -21968, 982332]$$ $$77860436/17787$$ $$267855713664000$$ $$[2]$$ $$884736$$ $$1.4809$$
323400.ct2 323400ct1 $$[0, -1, 0, -7268, -223068]$$ $$11279504/693$$ $$2608984224000$$ $$[2]$$ $$442368$$ $$1.1344$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 323400.ct have rank $$1$$.

## Complex multiplication

The elliptic curves in class 323400.ct do not have complex multiplication.

## Modular form 323400.2.a.ct

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.