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Properties

Label 235950ct
Number of curves $2$
Conductor $235950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 235950ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.ct2 235950ct1 \([1, 0, 1, -158876, 25639898]\) \(-16022066761/998400\) \(-27636351600000000\) \([2]\) \(2457600\) \(1.9089\) \(\Gamma_0(N)\)-optimal
235950.ct1 235950ct2 \([1, 0, 1, -2578876, 1593799898]\) \(68523370149961/243360\) \(6736360702500000\) \([2]\) \(4915200\) \(2.2555\)  

Rank

sage: E.rank()
 

The elliptic curves in class 235950ct have rank \(1\).

Complex multiplication

The elliptic curves in class 235950ct do not have complex multiplication.

Modular form 235950.2.a.ct

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