Properties

Label 7920bl
Number of curves $4$
Conductor $7920$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7920bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7920.y4 7920bl1 \([0, 0, 0, 1968, -123469]\) \(72268906496/606436875\) \(-7073479710000\) \([2]\) \(9216\) \(1.1470\) \(\Gamma_0(N)\)-optimal
7920.y3 7920bl2 \([0, 0, 0, -28407, -1696894]\) \(13584145739344/1195803675\) \(223165665043200\) \([2]\) \(18432\) \(1.4936\)  
7920.y2 7920bl3 \([0, 0, 0, -140592, -20306401]\) \(-26348629355659264/24169921875\) \(-281917968750000\) \([2]\) \(27648\) \(1.6963\)  
7920.y1 7920bl4 \([0, 0, 0, -2249967, -1299009526]\) \(6749703004355978704/5671875\) \(1058508000000\) \([2]\) \(55296\) \(2.0429\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7920.2.a.bl

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.