# Properties

 Label 92400.da Number of curves $2$ Conductor $92400$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("da1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.da

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.da1 92400bp2 $$[0, -1, 0, -52491208, -146361229088]$$ $$7997484869919944276/116700507$$ $$233401014000000000$$ $$[2]$$ $$5713920$$ $$2.8845$$
92400.da2 92400bp1 $$[0, -1, 0, -3283708, -2281669088]$$ $$7831544736466064/29831377653$$ $$14915688826500000000$$ $$[2]$$ $$2856960$$ $$2.5379$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 92400.da have rank $$0$$.

## Complex multiplication

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

## Modular form 92400.2.a.da

sage: E.q_eigenform(10)

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

## 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.