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Properties

Label 235950.ei
Number of curves $2$
Conductor $235950$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("ei1")
 
E.isogeny_class()
 

Elliptic curves in class 235950.ei

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.ei1 235950ei2 \([1, 0, 1, -426286, -106822432]\) \(38686490446661/141927552\) \(31429164493584000\) \([2]\) \(3870720\) \(2.0260\)  
235950.ei2 235950ei1 \([1, 0, 1, -39086, 44768]\) \(29819839301/17252352\) \(3820449245184000\) \([2]\) \(1935360\) \(1.6794\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 235950.ei have rank \(0\).

Complex multiplication

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

Modular form 235950.2.a.ei

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