Properties

Label 16900.e
Number of curves $2$
Conductor $16900$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 16900.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16900.e1 16900h2 \([0, -1, 0, -7258, -232363]\) \(1000939264/15625\) \(660156250000\) \([]\) \(20736\) \(1.0689\)  
16900.e2 16900h1 \([0, -1, 0, -758, 8137]\) \(1141504/25\) \(1056250000\) \([]\) \(6912\) \(0.51961\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 16900.e have rank \(2\).

Complex multiplication

The elliptic curves in class 16900.e do not have complex multiplication.

Modular form 16900.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} - 2 q^{9} - 3 q^{11} + 3 q^{17} - 5 q^{19} + O(q^{20})\) 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.