# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.s1 92400d1 $$[0, -1, 0, -157008, -23893488]$$ $$26752959989284/169785$$ $$2716560000000$$ $$[2]$$ $$479232$$ $$1.5709$$ $$\Gamma_0(N)$$-optimal
92400.s2 92400d2 $$[0, -1, 0, -154008, -24853488]$$ $$-12624273557282/1067664675$$ $$-34165269600000000$$ $$[2]$$ $$958464$$ $$1.9175$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92400.2.a.s

sage: E.q_eigenform(10)

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

## 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.