Properties

Label 22800.br
Number of curves $4$
Conductor $22800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 22800.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22800.br1 22800bv4 \([0, -1, 0, -196992008, -1064128873488]\) \(13209596798923694545921/92340\) \(5909760000000\) \([2]\) \(2211840\) \(2.9854\)  
22800.br2 22800bv3 \([0, -1, 0, -12464008, -16192233488]\) \(3345930611358906241/165622259047500\) \(10599824579040000000000\) \([2]\) \(2211840\) \(2.9854\)  
22800.br3 22800bv2 \([0, -1, 0, -12312008, -16623913488]\) \(3225005357698077121/8526675600\) \(545707238400000000\) \([2, 2]\) \(1105920\) \(2.6388\)  
22800.br4 22800bv1 \([0, -1, 0, -760008, -266281488]\) \(-758575480593601/40535043840\) \(-2594242805760000000\) \([2]\) \(552960\) \(2.2922\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22800.br have rank \(0\).

Complex multiplication

The elliptic curves in class 22800.br do not have complex multiplication.

Modular form 22800.2.a.br

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{7} + q^{9} + 6 q^{13} - 2 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.