Properties

Label 4410s
Number of curves $2$
Conductor $4410$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 4410s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.s2 4410s1 \([1, -1, 0, -639, -7155]\) \(-115501303/25600\) \(-6401203200\) \([2]\) \(3840\) \(0.60211\) \(\Gamma_0(N)\)-optimal
4410.s1 4410s2 \([1, -1, 0, -10719, -424467]\) \(544737993463/20000\) \(5000940000\) \([2]\) \(7680\) \(0.94868\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4410s have rank \(0\).

Complex multiplication

The elliptic curves in class 4410s do not have complex multiplication.

Modular form 4410.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} + 4 q^{11} - 2 q^{13} + q^{16} + 8 q^{17} + 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.