Properties

Label 11310.h
Number of curves $2$
Conductor $11310$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 11310.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11310.h1 11310h1 \([1, 1, 1, -9691, -123991]\) \(100654290922421809/52033093632000\) \(52033093632000\) \([2]\) \(38400\) \(1.3240\) \(\Gamma_0(N)\)-optimal
11310.h2 11310h2 \([1, 1, 1, 36389, -916567]\) \(5328847957372469711/3458851344000000\) \(-3458851344000000\) \([2]\) \(76800\) \(1.6705\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11310.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2 q^{7} + q^{8} + q^{9} - q^{10} + 2 q^{11} - q^{12} + q^{13} + 2 q^{14} + q^{15} + q^{16} - 2 q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.