Properties

Label 235950.ip
Number of curves $2$
Conductor $235950$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ip1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235950.ip

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.ip1 235950ip2 \([1, 0, 0, -139213, 17898167]\) \(10779215329/1232010\) \(34102826056406250\) \([2]\) \(2949120\) \(1.9046\)  
235950.ip2 235950ip1 \([1, 0, 0, 12037, 1411917]\) \(6967871/35100\) \(-971590485937500\) \([2]\) \(1474560\) \(1.5580\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.ip

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