Properties

Label 4410k
Number of curves $2$
Conductor $4410$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.c2 4410k1 \([1, -1, 0, -450, -138020]\) \(-49/40\) \(-8236978260840\) \([]\) \(10080\) \(1.1573\) \(\Gamma_0(N)\)-optimal
4410.c1 4410k2 \([1, -1, 0, -216540, -38731694]\) \(-5452947409/250\) \(-51481114130250\) \([]\) \(30240\) \(1.7066\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4410k have rank \(1\).

Complex multiplication

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

Modular form 4410.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 3q^{11} - 5q^{13} + q^{16} + 6q^{17} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.