# Properties

 Label 92400cx Number of curves $2$ Conductor $92400$ CM no Rank $0$ Graph

# Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 92400cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.gi2 92400cx1 $$[0, 1, 0, -131348, -18305892]$$ $$7831544736466064/29831377653$$ $$954604084896000$$ $$[2]$$ $$571392$$ $$1.7332$$ $$\Gamma_0(N)$$-optimal
92400.gi1 92400cx2 $$[0, 1, 0, -2099648, -1171729692]$$ $$7997484869919944276/116700507$$ $$14937664896000$$ $$[2]$$ $$1142784$$ $$2.0797$$

## Rank

sage: E.rank()

The elliptic curves in class 92400cx have rank $$0$$.

## Complex multiplication

The elliptic curves in class 92400cx do not have complex multiplication.

## Modular form 92400.2.a.cx

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} + q^{11} + 4 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})$$

## 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 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.