Properties

Label 19950.d
Number of curves $2$
Conductor $19950$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 19950.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19950.d1 19950j2 \([1, 1, 0, -81375, -7234875]\) \(3814038123905521/773540010432\) \(12086562663000000\) \([2]\) \(215040\) \(1.8016\)  
19950.d2 19950j1 \([1, 1, 0, -25375, 1445125]\) \(115650783909361/8339853312\) \(130310208000000\) \([2]\) \(107520\) \(1.4551\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 19950.d have rank \(0\).

Complex multiplication

The elliptic curves in class 19950.d do not have complex multiplication.

Modular form 19950.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 6 q^{11} - q^{12} + 4 q^{13} - q^{14} + q^{16} + 4 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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 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.