# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("gq1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.gq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.gq1 92400cl4 $$[0, 1, 0, -251533408, -1535554874812]$$ $$109999511474021786850916/38201625$$ $$611226000000000$$ $$[2]$$ $$8847360$$ $$3.0985$$
92400.gq2 92400cl2 $$[0, 1, 0, -15720908, -23996749812]$$ $$107422839278466723664/2001871265625$$ $$8007485062500000000$$ $$[2, 2]$$ $$4423680$$ $$2.7519$$
92400.gq3 92400cl3 $$[0, 1, 0, -15206408, -25640062812]$$ $$-24304331176056594436/3678122314453125$$ $$-58849957031250000000000$$ $$[2]$$ $$8847360$$ $$3.0985$$
92400.gq4 92400cl1 $$[0, 1, 0, -1014783, -349300812]$$ $$462278484549842944/57095309704125$$ $$14273827426031250000$$ $$[2]$$ $$2211840$$ $$2.4054$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92400.2.a.gq

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} - q^{11} - 6 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.