Properties

Label 1764.b
Number of curves $2$
Conductor $1764$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1764.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1764.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1764.b1 1764i2 [0, 0, 0, -19551, 974806] [2] 5376  
1764.b2 1764i1 [0, 0, 0, -4116, -84035] [2] 2688 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1764.b have rank \(0\).

Modular form 1764.2.a.b

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 2q^{11} - 4q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.