# Properties

 Label 92400cc Number of curves $4$ Conductor $92400$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cc1")

sage: E.isogeny_class()

## Elliptic curves in class 92400cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.fo3 92400cc1 $$[0, 1, 0, -1783, -25312]$$ $$2508888064/396165$$ $$99041250000$$ $$[2]$$ $$73728$$ $$0.83266$$ $$\Gamma_0(N)$$-optimal
92400.fo2 92400cc2 $$[0, 1, 0, -7908, 244188]$$ $$13674725584/1334025$$ $$5336100000000$$ $$[2, 2]$$ $$147456$$ $$1.1792$$
92400.fo4 92400cc3 $$[0, 1, 0, 9592, 1189188]$$ $$6099383804/41507235$$ $$-664115760000000$$ $$[4]$$ $$294912$$ $$1.5258$$
92400.fo1 92400cc4 $$[0, 1, 0, -123408, 16645188]$$ $$12990838708516/144375$$ $$2310000000000$$ $$[2]$$ $$294912$$ $$1.5258$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92400.2.a.cc

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} + q^{11} - 2 q^{13} - 6 q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.