# Properties

 Label 101400.do Number of curves $4$ Conductor $101400$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 101400.do

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101400.do1 101400di4 $$[0, 1, 0, -35153408, 80211350688]$$ $$31103978031362/195$$ $$30119288160000000$$ $$[2]$$ $$6193152$$ $$2.7676$$
101400.do2 101400di3 $$[0, 1, 0, -3043408, 199990688]$$ $$20183398562/11567205$$ $$1786646054363040000000$$ $$[2]$$ $$6193152$$ $$2.7676$$
101400.do3 101400di2 $$[0, 1, 0, -2198408, 1251170688]$$ $$15214885924/38025$$ $$2936630595600000000$$ $$[2, 2]$$ $$3096576$$ $$2.4210$$
101400.do4 101400di1 $$[0, 1, 0, -85908, 34370688]$$ $$-3631696/24375$$ $$-470613877500000000$$ $$[2]$$ $$1548288$$ $$2.0744$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 101400.do have rank $$1$$.

## Complex multiplication

The elliptic curves in class 101400.do do not have complex multiplication.

## Modular form 101400.2.a.do

sage: E.q_eigenform(10)

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

## 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.