# Properties

 Label 138600.di Number of curves $4$ Conductor $138600$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("di1")

sage: E.isogeny_class()

## Elliptic curves in class 138600.di

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
138600.di1 138600bf4 $$[0, 0, 0, -6699675, -6673558250]$$ $$1425631925916578/270703125$$ $$6314962500000000000$$ $$[2]$$ $$3145728$$ $$2.6086$$
138600.di2 138600bf3 $$[0, 0, 0, -2937675, 1876675750]$$ $$120186986927618/4332064275$$ $$101058395407200000000$$ $$[2]$$ $$3145728$$ $$2.6086$$
138600.di3 138600bf2 $$[0, 0, 0, -462675, -81049250]$$ $$939083699236/300155625$$ $$3501015210000000000$$ $$[2, 2]$$ $$1572864$$ $$2.2620$$
138600.di4 138600bf1 $$[0, 0, 0, 81825, -8630750]$$ $$20777545136/23059575$$ $$-67241720700000000$$ $$[2]$$ $$786432$$ $$1.9154$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 138600.di have rank $$0$$.

## Complex multiplication

The elliptic curves in class 138600.di do not have complex multiplication.

## Modular form 138600.2.a.di

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.