Properties

Label 11310n
Number of curves $4$
Conductor $11310$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 11310n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11310.m4 11310n1 \([1, 0, 0, -28315, 523217]\) \(2510581756496128561/1333551278592000\) \(1333551278592000\) \([4]\) \(69120\) \(1.5936\) \(\Gamma_0(N)\)-optimal
11310.m2 11310n2 \([1, 0, 0, -261595, -51124975]\) \(1979758117698975186481/17510434929000000\) \(17510434929000000\) \([2, 2]\) \(138240\) \(1.9402\)  
11310.m1 11310n3 \([1, 0, 0, -4176595, -3285697975]\) \(8057323694463985606146481/638717154543000\) \(638717154543000\) \([2]\) \(276480\) \(2.2868\)  
11310.m3 11310n4 \([1, 0, 0, -79075, -121103143]\) \(-54681655838565466801/6303365630859375000\) \(-6303365630859375000\) \([2]\) \(276480\) \(2.2868\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11310n have rank \(1\).

Complex multiplication

The elliptic curves in class 11310n do not have complex multiplication.

Modular form 11310.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{8} + q^{9} + q^{10} - 4 q^{11} + q^{12} - q^{13} + q^{15} + q^{16} + 2 q^{17} + q^{18} + O(q^{20})\) 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 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.