Properties

Label 7920k
Number of curves $2$
Conductor $7920$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 7920k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7920.bg1 7920k1 \([0, 0, 0, -342, -2349]\) \(379275264/15125\) \(176418000\) \([2]\) \(3072\) \(0.34888\) \(\Gamma_0(N)\)-optimal
7920.bg2 7920k2 \([0, 0, 0, 153, -8586]\) \(2122416/171875\) \(-32076000000\) \([2]\) \(6144\) \(0.69545\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7920k have rank \(1\).

Complex multiplication

The elliptic curves in class 7920k do not have complex multiplication.

Modular form 7920.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{7} - q^{11} + 8 q^{19} + O(q^{20})\) 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.