Properties

Label 77616by
Number of curves $2$
Conductor $77616$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 77616by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77616.gs1 77616by1 \([0, 0, 0, -3535203, 2558406130]\) \(55635379958596/24057\) \(2112794186646528\) \([2]\) \(1935360\) \(2.2830\) \(\Gamma_0(N)\)-optimal
77616.gs2 77616by2 \([0, 0, 0, -3517563, 2585201290]\) \(-27403349188178/578739249\) \(-101654979496311048192\) \([2]\) \(3870720\) \(2.6295\)  

Rank

sage: E.rank()
 

The elliptic curves in class 77616by have rank \(1\).

Complex multiplication

The elliptic curves in class 77616by do not have complex multiplication.

Modular form 77616.2.a.by

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