↑

Properties

Label 372810.n
Number of curves $4$
Conductor $372810$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 372810.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372810.n1 372810n3 \([1, 1, 0, -242332, 45502114]\) \(65202655558249/512820150\) \(12378231755215350\) \([2]\) \(3932160\) \(1.9161\)  
372810.n2 372810n2 \([1, 1, 0, -25582, -405536]\) \(76711450249/41602500\) \(1004183214322500\) \([2, 2]\) \(1966080\) \(1.5695\)  
372810.n3 372810n1 \([1, 1, 0, -19802, -1079484]\) \(35578826569/51600\) \(1245498560400\) \([2]\) \(983040\) \(1.2229\) \(\Gamma_0(N)\)-optimal
372810.n4 372810n4 \([1, 1, 0, 98688, -3064914]\) \(4403686064471/2721093750\) \(-65680588146093750\) \([2]\) \(3932160\) \(1.9161\)  

Rank

sage: E.rank()
 

The elliptic curves in class 372810.n have rank \(2\).

Complex multiplication

The elliptic curves in class 372810.n do not have complex multiplication.

Modular form 372810.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{10} - q^{12} - 2 q^{13} + 4 q^{14} - q^{15} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.