Properties

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

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

Elliptic curves in class 4410.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.m1 4410o2 \([1, -1, 0, -4419, 114183]\) \(-5452947409/250\) \(-437582250\) \([3]\) \(4320\) \(0.73370\)  
4410.m2 4410o1 \([1, -1, 0, -9, 405]\) \(-49/40\) \(-70013160\) \([]\) \(1440\) \(0.18439\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4410.2.a.m

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