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Properties

Label 235950ib
Number of curves $2$
Conductor $235950$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("ib1")
 
E.isogeny_class()
 

Elliptic curves in class 235950ib

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.ib2 235950ib1 \([1, 0, 0, -1878, 27072]\) \(3307949/468\) \(103636318500\) \([2]\) \(276480\) \(0.83962\) \(\Gamma_0(N)\)-optimal
235950.ib1 235950ib2 \([1, 0, 0, -7928, -245178]\) \(248858189/27378\) \(6062724632250\) \([2]\) \(552960\) \(1.1862\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.ib

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