# Properties

 Label 33810.v Number of curves $4$ Conductor $33810$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 33810.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33810.v1 33810t4 $$[1, 1, 0, -147718267, -1957264931]$$ $$3029968325354577848895529/1753440696000000000000$$ $$206290544443704000000000000$$ $$$$ $$13271040$$ $$3.7387$$
33810.v2 33810t2 $$[1, 1, 0, -101618332, -394321479824]$$ $$986396822567235411402169/6336721794060000$$ $$745508982349364940000$$ $$$$ $$4423680$$ $$3.1894$$
33810.v3 33810t1 $$[1, 1, 0, -6229052, -6411433776]$$ $$-227196402372228188089/19338934824115200$$ $$-2275206343122329164800$$ $$$$ $$2211840$$ $$2.8429$$ $$\Gamma_0(N)$$-optimal
33810.v4 33810t3 $$[1, 1, 0, 36929413, -221576739]$$ $$47342661265381757089751/27397579603968000000$$ $$-3223297842827231232000000$$ $$$$ $$6635520$$ $$3.3922$$

## Rank

sage: E.rank()

The elliptic curves in class 33810.v have rank $$0$$.

## Complex multiplication

The elliptic curves in class 33810.v do not have complex multiplication.

## Modular form 33810.2.a.v

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{12} + 4q^{13} - q^{15} + q^{16} - q^{18} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 