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Properties

Label 235950i
Number of curves $2$
Conductor $235950$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 235950i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.i2 235950i1 \([1, 1, 0, -839500, 585394000]\) \(-1775956931/2995200\) \(-110351951938800000000\) \([2]\) \(13178880\) \(2.5366\) \(\Gamma_0(N)\)-optimal
235950.i1 235950i2 \([1, 1, 0, -16811500, 26507950000]\) \(14262279885251/10140000\) \(373587337292812500000\) \([2]\) \(26357760\) \(2.8831\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.i

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