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Properties

Label 360789e
Number of curves $2$
Conductor $360789$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 360789e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
360789.e2 360789e1 \([1, 0, 0, -9005742131, -330371723572032]\) \(-135798272907989852399888089/681332888130948168687\) \(-405272691224572072577269549527\) \([2]\) \(955100160\) \(4.5285\) \(\Gamma_0(N)\)-optimal
360789.e1 360789e2 \([1, 0, 0, -144264936916, -21090629235147757]\) \(558236327843639730114488861929/13948140496113173493\) \(8296679251672625448955430253\) \([2]\) \(1910200320\) \(4.8750\)  

Rank

sage: E.rank()
 

The elliptic curves in class 360789e have rank \(0\).

Complex multiplication

The elliptic curves in class 360789e do not have complex multiplication.

Modular form 360789.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} + 4 q^{5} - q^{6} + 4 q^{7} + 3 q^{8} + q^{9} - 4 q^{10} - q^{11} - q^{12} - q^{13} - 4 q^{14} + 4 q^{15} - q^{16} + 2 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.