Properties

Label 369600.iq
Number of curves $2$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("iq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.iq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.iq1 369600iq1 \([0, -1, 0, -36008, 2481762]\) \(5163364362304/352983015\) \(352983015000000\) \([2]\) \(1720320\) \(1.5398\) \(\Gamma_0(N)\)-optimal
369600.iq2 369600iq2 \([0, -1, 0, 31367, 10634137]\) \(53327207744/795685275\) \(-50923857600000000\) \([2]\) \(3440640\) \(1.8864\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.iq have rank \(0\).

Complex multiplication

The elliptic curves in class 369600.iq do not have complex multiplication.

Modular form 369600.2.a.iq

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