Properties

 Label 333270.db Number of curves $4$ Conductor $333270$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("db1")

sage: E.isogeny_class()

Elliptic curves in class 333270.db

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.db1 333270db4 $$[1, -1, 1, -14352789218, 1819214009057]$$ $$3029968325354577848895529/1753440696000000000000$$ $$189228098983790144376000000000000$$ $$[2]$$ $$1167851520$$ $$4.8828$$
333270.db2 333270db2 $$[1, -1, 1, -9873569003, 377624175754331]$$ $$986396822567235411402169/6336721794060000$$ $$683847375970293977098860000$$ $$[2]$$ $$389283840$$ $$4.3335$$
333270.db3 333270db1 $$[1, -1, 1, -605235083, 6138230240027]$$ $$-227196402372228188089/19338934824115200$$ $$-2087022322161694205130931200$$ $$[2]$$ $$194641920$$ $$3.9870$$ $$\Gamma_0(N)$$-optimal
333270.db4 333270db3 $$[1, -1, 1, 3588182302, 226055738081]$$ $$47342661265381757089751/27397579603968000000$$ $$-2956696463725698018705408000000$$ $$[2]$$ $$583925760$$ $$4.5363$$

Rank

sage: E.rank()

The elliptic curves in class 333270.db have rank $$0$$.

Complex multiplication

The elliptic curves in class 333270.db do not have complex multiplication.

Modular form 333270.2.a.db

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} - 4q^{13} - q^{14} + q^{16} - 2q^{19} + O(q^{20})$$

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.