Properties

Label 4235b
Number of curves $3$
Conductor $4235$
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 4235b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4235.c2 4235b1 \([0, 1, 1, -161, -929]\) \(-262144/35\) \(-62004635\) \([]\) \(900\) \(0.22780\) \(\Gamma_0(N)\)-optimal
4235.c3 4235b2 \([0, 1, 1, 1049, 2580]\) \(71991296/42875\) \(-75955677875\) \([]\) \(2700\) \(0.77710\)  
4235.c1 4235b3 \([0, 1, 1, -15891, 801301]\) \(-250523582464/13671875\) \(-24220560546875\) \([]\) \(8100\) \(1.3264\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4235b have rank \(0\).

Complex multiplication

The elliptic curves in class 4235b do not have complex multiplication.

Modular form 4235.2.a.b

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