Properties

Label 35131.b
Number of curves $3$
Conductor $35131$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35131.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35131.b1 35131c3 \([0, -1, 1, -1422497, 653492395]\) \(-50357871050752/19\) \(-120105897931\) \([]\) \(243810\) \(1.9140\)  
35131.b2 35131c2 \([0, -1, 1, -17257, 934070]\) \(-89915392/6859\) \(-43358229153091\) \([]\) \(81270\) \(1.3647\)  
35131.b3 35131c1 \([0, -1, 1, 1233, 325]\) \(32768/19\) \(-120105897931\) \([]\) \(27090\) \(0.81543\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35131.b have rank \(0\).

Complex multiplication

The elliptic curves in class 35131.b do not have complex multiplication.

Modular form 35131.2.a.b

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