Properties

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

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 235950.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.v1 235950v2 \([1, 1, 0, -1669916525, 26265193405125]\) \(-18605093748570727251049/91759078125000\) \(-2539950065659423828125000\) \([]\) \(130636800\) \(3.8823\)  
235950.v2 235950v1 \([1, 1, 0, -12322400, 65220236250]\) \(-7475384530020889/62069784455250\) \(-1718131397176986644531250\) \([]\) \(43545600\) \(3.3330\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.v

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