# Properties

 Label 92400.cp Number of curves $2$ Conductor $92400$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cp1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.cp1 92400bm2 $$[0, -1, 0, -448, 2992]$$ $$77860436/17787$$ $$2276736000$$ $$[2]$$ $$36864$$ $$0.50799$$
92400.cp2 92400bm1 $$[0, -1, 0, -148, -608]$$ $$11279504/693$$ $$22176000$$ $$[2]$$ $$18432$$ $$0.16142$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 92400.cp have rank $$1$$.

## Complex multiplication

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

## Modular form 92400.2.a.cp

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} - q^{11} + 4 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.