Properties

Label 360.d
Number of curves $2$
Conductor $360$
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 360.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
360.d1 360c2 \([0, 0, 0, -1107, 14094]\) \(3721734/25\) \(1007769600\) \([2]\) \(192\) \(0.56230\)  
360.d2 360c1 \([0, 0, 0, -27, 486]\) \(-108/5\) \(-100776960\) \([2]\) \(96\) \(0.21572\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 360.d have rank \(0\).

Complex multiplication

The elliptic curves in class 360.d do not have complex multiplication.

Modular form 360.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2q^{7} - 2q^{11} + 4q^{13} + 2q^{17} + 4q^{19} + O(q^{20})\)  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.