Properties

Label 22320cb
Number of curves $4$
Conductor $22320$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 22320cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22320.bm3 22320cb1 \([0, 0, 0, -15627, -668486]\) \(141339344329/17141760\) \(51185021091840\) \([2]\) \(55296\) \(1.3610\) \(\Gamma_0(N)\)-optimal
22320.bm2 22320cb2 \([0, 0, 0, -61707, 5202106]\) \(8702409880009/1120910400\) \(3347020519833600\) \([2, 2]\) \(110592\) \(1.7076\)  
22320.bm4 22320cb3 \([0, 0, 0, 93813, 27192634]\) \(30579142915511/124675335000\) \(-372278555504640000\) \([4]\) \(221184\) \(2.0542\)  
22320.bm1 22320cb4 \([0, 0, 0, -954507, 358929466]\) \(32208729120020809/658986840\) \(1967724160450560\) \([2]\) \(221184\) \(2.0542\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22320cb have rank \(1\).

Complex multiplication

The elliptic curves in class 22320cb do not have complex multiplication.

Modular form 22320.2.a.cb

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{11} + 6 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.