Properties

Label 3600.q
Number of curves $2$
Conductor $3600$
CM \(\Q(\sqrt{-3}) \)
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 3600.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
3600.q1 3600y1 \([0, 0, 0, 0, -12500]\) \(0\) \(-67500000000\) \([]\) \(2880\) \(0.75683\) \(\Gamma_0(N)\)-optimal \(-3\)
3600.q2 3600y2 \([0, 0, 0, 0, 337500]\) \(0\) \(-49207500000000\) \([]\) \(8640\) \(1.3061\)   \(-3\)

Rank

sage: E.rank()
 

The elliptic curves in class 3600.q have rank \(0\).

Complex multiplication

Each elliptic curve in class 3600.q has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 3600.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{7} + 7 q^{13} + 7 q^{19} + O(q^{20})\) 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.