Properties

Label 79560.w
Number of curves $2$
Conductor $79560$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 79560.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79560.w1 79560bn1 \([0, 0, 0, -963, 2862]\) \(132304644/71825\) \(53617075200\) \([2]\) \(65536\) \(0.74968\) \(\Gamma_0(N)\)-optimal
79560.w2 79560bn2 \([0, 0, 0, 3717, 22518]\) \(3804029838/2348125\) \(-3505731840000\) \([2]\) \(131072\) \(1.0963\)  

Rank

sage: E.rank()
 

The elliptic curves in class 79560.w have rank \(1\).

Complex multiplication

The elliptic curves in class 79560.w do not have complex multiplication.

Modular form 79560.2.a.w

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