Properties

Label 3600.d
Number of curves $2$
Conductor $3600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3600.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.d1 3600br1 \([0, 0, 0, -3000, 59375]\) \(131072/9\) \(205031250000\) \([2]\) \(3840\) \(0.91877\) \(\Gamma_0(N)\)-optimal
3600.d2 3600br2 \([0, 0, 0, 2625, 256250]\) \(5488/81\) \(-29524500000000\) \([2]\) \(7680\) \(1.2653\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 3600.d do not have complex multiplication.

Modular form 3600.2.a.d

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