Properties

Label 22080.bv
Number of curves $6$
Conductor $22080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 22080.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22080.bv1 22080cr4 \([0, 1, 0, -7065601, -7231248385]\) \(148809678420065817601/20700\) \(5426380800\) \([2]\) \(294912\) \(2.1927\)  
22080.bv2 22080cr6 \([0, 1, 0, -1653121, 700222079]\) \(1905890658841300321/293666194803750\) \(76982830970634240000\) \([2]\) \(589824\) \(2.5393\)  
22080.bv3 22080cr3 \([0, 1, 0, -453121, -106897921]\) \(39248884582600321/3935264062500\) \(1031605862400000000\) \([2, 2]\) \(294912\) \(2.1927\)  
22080.bv4 22080cr2 \([0, 1, 0, -441601, -113097985]\) \(36330796409313601/428490000\) \(112326082560000\) \([2, 2]\) \(147456\) \(1.8462\)  
22080.bv5 22080cr1 \([0, 1, 0, -26881, -1870081]\) \(-8194759433281/965779200\) \(-253173222604800\) \([2]\) \(73728\) \(1.4996\) \(\Gamma_0(N)\)-optimal
22080.bv6 22080cr5 \([0, 1, 0, 562559, -517029505]\) \(75108181893694559/484313964843750\) \(-126960000000000000000\) \([2]\) \(589824\) \(2.5393\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22080.bv have rank \(0\).

Complex multiplication

The elliptic curves in class 22080.bv do not have complex multiplication.

Modular form 22080.2.a.bv

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + 4 q^{11} + 2 q^{13} - q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.