# Properties

 Label 93600cx Number of curves $2$ Conductor $93600$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cx1")

sage: E.isogeny_class()

## Elliptic curves in class 93600cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.g2 93600cx1 $$[0, 0, 0, 75, -4500]$$ $$1728/325$$ $$-8775000000$$ $$[2]$$ $$49152$$ $$0.58718$$ $$\Gamma_0(N)$$-optimal
93600.g1 93600cx2 $$[0, 0, 0, -3675, -83250]$$ $$25412184/845$$ $$182520000000$$ $$[2]$$ $$98304$$ $$0.93375$$

## Rank

sage: E.rank()

The elliptic curves in class 93600cx have rank $$1$$.

## Complex multiplication

The elliptic curves in class 93600cx do not have complex multiplication.

## Modular form 93600.2.a.cx

sage: E.q_eigenform(10)

$$q - 4q^{7} - 4q^{11} + q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.