↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 235950d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.d2 235950d1 \([1, 1, 0, -355500, -260698500]\) \(-179501589721/955597500\) \(-26451550979648437500\) \([2]\) \(7372800\) \(2.4110\) \(\Gamma_0(N)\)-optimal
235950.d1 235950d2 \([1, 1, 0, -8674250, -9818942250]\) \(2607614922465721/5488604550\) \(151928090081289843750\) \([2]\) \(14745600\) \(2.7576\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 235950.2.a.d

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