↑

Properties

Label 35574.bl
Number of curves $2$
Conductor $35574$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 35574.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35574.bl1 35574bm2 \([1, 0, 1, -44141529, 112848206524]\) \(45637459887836881/13417633152\) \(2796535036700911110528\) \([2]\) \(7741440\) \(3.0942\)  
35574.bl2 35574bm1 \([1, 0, 1, -2401369, 2236782524]\) \(-7347774183121/6119866368\) \(-1275517114245183946752\) \([2]\) \(3870720\) \(2.7477\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35574.bl have rank \(0\).

Complex multiplication

The elliptic curves in class 35574.bl do not have complex multiplication.

Modular form 35574.2.a.bl

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 4 q^{5} - q^{6} - q^{8} + q^{9} - 4 q^{10} + q^{12} - 6 q^{13} + 4 q^{15} + q^{16} - 4 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.