Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11310.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11310.f1 11310f1 \([1, 0, 1, -833, 7796]\) \(63812982460681/10201800960\) \(10201800960\) \([2]\) \(7680\) \(0.64290\) \(\Gamma_0(N)\)-optimal
11310.f2 11310f2 \([1, 0, 1, 1487, 43988]\) \(363979050334199/1041836936400\) \(-1041836936400\) \([2]\) \(15360\) \(0.98947\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11310.2.a.f

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