Properties

Label 4410m
Number of curves $4$
Conductor $4410$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4410m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.b4 4410m1 \([1, -1, 0, 1020, -20224]\) \(1367631/2800\) \(-240145138800\) \([2]\) \(6144\) \(0.86810\) \(\Gamma_0(N)\)-optimal
4410.b3 4410m2 \([1, -1, 0, -7800, -212500]\) \(611960049/122500\) \(10506349822500\) \([2, 2]\) \(12288\) \(1.2147\)  
4410.b1 4410m3 \([1, -1, 0, -118050, -15581350]\) \(2121328796049/120050\) \(10296222826050\) \([2]\) \(24576\) \(1.5612\)  
4410.b2 4410m4 \([1, -1, 0, -38670, 2744846]\) \(74565301329/5468750\) \(469033474218750\) \([2]\) \(24576\) \(1.5612\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4410.2.a.m

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.