# Properties

 Label 92400.do Number of curves $2$ Conductor $92400$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("do1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.do

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.do1 92400u1 $$[0, -1, 0, -3008, -61488]$$ $$188183524/3465$$ $$55440000000$$ $$$$ $$110592$$ $$0.85617$$ $$\Gamma_0(N)$$-optimal
92400.do2 92400u2 $$[0, -1, 0, -8, -181488]$$ $$-2/444675$$ $$-14229600000000$$ $$$$ $$221184$$ $$1.2027$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92400.2.a.do

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} + q^{11} - 8 q^{17} - 8 q^{19} + O(q^{20})$$ ## 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. 