Properties

Label 397800.cb
Number of curves $4$
Conductor $397800$
CM no
Rank $1$
Graph

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

Elliptic curves in class 397800.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
397800.cb1 397800cb3 \([0, 0, 0, -14061675, 20295521750]\) \(26362547147244676/244298925\) \(2849502661200000000\) \([2]\) \(14155776\) \(2.7048\)  
397800.cb2 397800cb2 \([0, 0, 0, -899175, 301684250]\) \(27572037674704/2472575625\) \(7210030522500000000\) \([2, 2]\) \(7077888\) \(2.3582\)  
397800.cb3 397800cb1 \([0, 0, 0, -196050, -28081375]\) \(4572531595264/776953125\) \(141599707031250000\) \([2]\) \(3538944\) \(2.0117\) \(\Gamma_0(N)\)-optimal
397800.cb4 397800cb4 \([0, 0, 0, 1013325, 1412846750]\) \(9865576607324/79640206425\) \(-928923367741200000000\) \([2]\) \(14155776\) \(2.7048\)  

Rank

sage: E.rank()
 

The elliptic curves in class 397800.cb have rank \(1\).

Complex multiplication

The elliptic curves in class 397800.cb do not have complex multiplication.

Modular form 397800.2.a.cb

sage: E.q_eigenform(10)
 
\(q - 4q^{11} - q^{13} + q^{17} - 8q^{19} + O(q^{20})\)  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.