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Properties

Label 233450.bd
Number of curves $2$
Conductor $233450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 233450.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
233450.bd1 233450bd2 \([1, 1, 0, -13475275, 16550248125]\) \(17318754151497695091889/2444204545180160000\) \(38190696018440000000000\) \([2]\) \(30081024\) \(3.0591\)  
233450.bd2 233450bd1 \([1, 1, 0, 1372725, 1390440125]\) \(18308544547638944591/64003790130380800\) \(-1000059220787200000000\) \([2]\) \(15040512\) \(2.7125\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 233450.bd have rank \(1\).

Complex multiplication

The elliptic curves in class 233450.bd do not have complex multiplication.

Modular form 233450.2.a.bd

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} - q^{7} - q^{8} + q^{9} - 4 q^{11} + 2 q^{12} + 2 q^{13} + q^{14} + q^{16} + 8 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.