Properties

Label 274890.cb
Number of curves $4$
Conductor $274890$
CM no
Rank $1$
Graph

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

Elliptic curves in class 274890.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.cb1 274890cb4 \([1, 0, 1, -18468469, -29645136958]\) \(5921450764096952391481/200074809015963750\) \(23538601205919119223750\) \([2]\) \(28311552\) \(3.0651\)  
274890.cb2 274890cb2 \([1, 0, 1, -2849719, 1211265542]\) \(21754112339458491481/7199734626562500\) \(847041579080451562500\) \([2, 2]\) \(14155776\) \(2.7185\)  
274890.cb3 274890cb1 \([1, 0, 1, -2566499, 1582057166]\) \(15891267085572193561/3334993530000\) \(392358653810970000\) \([2]\) \(7077888\) \(2.3719\) \(\Gamma_0(N)\)-optimal
274890.cb4 274890cb3 \([1, 0, 1, 8237511, 8338136986]\) \(525440531549759128199/559322204589843750\) \(-65803698047790527343750\) \([2]\) \(28311552\) \(3.0651\)  

Rank

sage: E.rank()
 

The elliptic curves in class 274890.cb have rank \(1\).

Complex multiplication

The elliptic curves in class 274890.cb do not have complex multiplication.

Modular form 274890.2.a.cb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - 2 q^{13} - q^{15} + q^{16} + q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.