Properties

Label 931.a
Number of curves $3$
Conductor $931$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 931.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
931.a1 931b3 \([0, -1, 1, -37697, 2829742]\) \(-50357871050752/19\) \(-2235331\) \([]\) \(1134\) \(1.0064\)  
931.a2 931b2 \([0, -1, 1, -457, 4157]\) \(-89915392/6859\) \(-806954491\) \([]\) \(378\) \(0.45709\)  
931.a3 931b1 \([0, -1, 1, 33, -8]\) \(32768/19\) \(-2235331\) \([]\) \(126\) \(-0.092218\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 931.a have rank \(0\).

Complex multiplication

The elliptic curves in class 931.a do not have complex multiplication.

Modular form 931.2.a.a

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.