Properties

Label 235200co
Number of curves $4$
Conductor $235200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.co4 235200co1 \([0, -1, 0, -1960191508, 32993938276762]\) \(7079962908642659949376/100085966990454375\) \(11775013930459966764375000000\) \([2]\) \(247726080\) \(4.1911\) \(\Gamma_0(N)\)-optimal
235200.co2 235200co2 \([0, -1, 0, -31255876633, 2126903032586137]\) \(448487713888272974160064/91549016015625\) \(689321611854225000000000000\) \([2, 2]\) \(495452160\) \(4.5377\)  
235200.co1 235200co3 \([0, -1, 0, -500094001633, 136121307995711137]\) \(229625675762164624948320008/9568125\) \(576348333120000000000\) \([2]\) \(990904320\) \(4.8842\)  
235200.co3 235200co4 \([0, -1, 0, -31148713633, 2142211374299137]\) \(-55486311952875723077768/801237030029296875\) \(-48263544497109375000000000000000\) \([2]\) \(990904320\) \(4.8842\)  

Rank

sage: E.rank()
 

The elliptic curves in class 235200co have rank \(1\).

Complex multiplication

The elliptic curves in class 235200co do not have complex multiplication.

Modular form 235200.2.a.co

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