Properties

Label 21904.d
Number of curves $3$
Conductor $21904$
CM no
Rank $0$
Graph

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

Elliptic curves in class 21904.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21904.d1 21904h3 \([0, -1, 0, -41033493, 101184633181]\) \(727057727488000/37\) \(388840968736768\) \([]\) \(590976\) \(2.7207\)  
21904.d2 21904h2 \([0, -1, 0, -511093, 136355645]\) \(1404928000/50653\) \(532323286200635392\) \([]\) \(196992\) \(2.1714\)  
21904.d3 21904h1 \([0, -1, 0, -73013, -7509827]\) \(4096000/37\) \(388840968736768\) \([]\) \(65664\) \(1.6221\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 21904.d have rank \(0\).

Complex multiplication

The elliptic curves in class 21904.d do not have complex multiplication.

Modular form 21904.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} - 2 q^{9} - 3 q^{11} + 4 q^{13} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.