Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 4410.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.h1 4410i1 \([1, -1, 0, -1185, 16001]\) \(-5154200289/20\) \(-714420\) \([]\) \(1680\) \(0.33648\) \(\Gamma_0(N)\)-optimal
4410.h2 4410i2 \([1, -1, 0, 8265, -151075]\) \(1747829720511/1280000000\) \(-45722880000000\) \([]\) \(11760\) \(1.3094\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4410.2.a.h

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.