Properties

Label 441090.m
Number of curves $2$
Conductor $441090$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 441090.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
441090.m1 441090m1 \([1, -1, 0, -758250, -253437404]\) \(13701674594089/31758480\) \(111749953358843280\) \([2]\) \(7569408\) \(2.1520\) \(\Gamma_0(N)\)-optimal
441090.m2 441090m2 \([1, -1, 0, -484470, -439115000]\) \(-3573857582569/21617820900\) \(-76067572418290404900\) \([2]\) \(15138816\) \(2.4985\)  

Rank

sage: E.rank()
 

The elliptic curves in class 441090.m have rank \(1\).

Complex multiplication

The elliptic curves in class 441090.m do not have complex multiplication.

Modular form 441090.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + 2 q^{7} - q^{8} + q^{10} - 2 q^{11} - 2 q^{14} + q^{16} + 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.