Properties

Label 193600w
Number of curves 2
Conductor 193600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("193600.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193600w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.bd2 193600w1 [0, 1, 0, -4033, 384063] [] 430080 \(\Gamma_0(N)\)-optimal
193600.bd1 193600w2 [0, 1, 0, -5812033, -5395247937] [] 4730880  

Rank

sage: E.rank()
 

The elliptic curves in class 193600w have rank \(1\).

Modular form 193600.2.a.bd

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - 2q^{7} + q^{9} + q^{13} + 5q^{17} + 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.