Properties

Label 4410.l
Number of curves $6$
Conductor $4410$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 4410.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.l1 4410t5 \([1, -1, 0, -7408809, -7760095785]\) \(524388516989299201/3150\) \(270163281150\) \([2]\) \(98304\) \(2.2590\)  
4410.l2 4410t3 \([1, -1, 0, -463059, -121159935]\) \(128031684631201/9922500\) \(851014335622500\) \([2, 2]\) \(49152\) \(1.9124\)  
4410.l3 4410t6 \([1, -1, 0, -432189, -138033477]\) \(-104094944089921/35880468750\) \(-3077328624349218750\) \([2]\) \(98304\) \(2.2590\)  
4410.l4 4410t4 \([1, -1, 0, -163179, 24020793]\) \(5602762882081/345888060\) \(29665477206415260\) \([2]\) \(49152\) \(1.9124\)  
4410.l5 4410t2 \([1, -1, 0, -30879, -1618947]\) \(37966934881/8643600\) \(741328043475600\) \([2, 2]\) \(24576\) \(1.5659\)  
4410.l6 4410t1 \([1, -1, 0, 4401, -158355]\) \(109902239/188160\) \(-16137753327360\) \([2]\) \(12288\) \(1.2193\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4410.2.a.l

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.