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Properties

Label 77763.bc
Number of curves $2$
Conductor $77763$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 77763.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77763.bc1 77763q2 \([0, -1, 1, -482624, -128993971]\) \(-1713910976512/1594323\) \(-11564834110249203\) \([]\) \(988416\) \(2.0051\)  
77763.bc2 77763q1 \([0, -1, 1, -1234, 18549]\) \(-28672/3\) \(-21761275683\) \([]\) \(76032\) \(0.72266\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 77763.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 77763.bc do not have complex multiplication.

Modular form 77763.2.a.bc

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{9} - 4 q^{10} + 2 q^{11} - 2 q^{12} - q^{13} + 2 q^{15} - 4 q^{16} + 2 q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.