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Properties

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

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Show commands: SageMath
E = EllipticCurve("gp1")
 
E.isogeny_class()
 

Elliptic curves in class 235950gp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.gp2 235950gp1 \([1, 1, 1, 256592537, -2265976710469]\) \(557820238477845431/985142146218750\) \(-3299593251396712987792968750\) \([]\) \(205286400\) \(3.9651\) \(\Gamma_0(N)\)-optimal
235950.gp1 235950gp2 \([1, 1, 1, -8678244088, -312371030504719]\) \(-21580315425730848803929/96405029296875000\) \(-322894909419536590576171875000\) \([]\) \(615859200\) \(4.5145\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.gp

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