Properties

Label 7920.bj
Number of curves $2$
Conductor $7920$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7920.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7920.bj1 7920q2 \([0, 0, 0, -15447, 485894]\) \(2184181167184/717482205\) \(133899399025920\) \([2]\) \(24576\) \(1.4137\)  
7920.bj2 7920q1 \([0, 0, 0, 2778, 52139]\) \(203269830656/218317275\) \(-2546452695600\) \([2]\) \(12288\) \(1.0671\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7920.bj have rank \(0\).

Complex multiplication

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

Modular form 7920.2.a.bj

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{7} + q^{11} + 8 q^{17} + 8 q^{19} + O(q^{20})\)  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.