Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 235950f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.f2 235950f1 \([1, 1, 0, 1450, 458220]\) \(7604375/2047032\) \(-90661051423800\) \([]\) \(933120\) \(1.3574\) \(\Gamma_0(N)\)-optimal
235950.f1 235950f2 \([1, 1, 0, -406925, 99758685]\) \(-168256703745625/30371328\) \(-1345116505075200\) \([]\) \(2799360\) \(1.9067\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{12} + q^{13} + 4 q^{14} + q^{16} - q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.