Properties

Label 366912.et
Number of curves $4$
Conductor $366912$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("et1")
 
E.isogeny_class()
 

Elliptic curves in class 366912.et

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
366912.et1 366912et4 \([0, 0, 0, -11769996, -15541889776]\) \(8020417344913/187278\) \(4210585136958799872\) \([2]\) \(14155776\) \(2.6860\)  
366912.et2 366912et2 \([0, 0, 0, -762636, -224047600]\) \(2181825073/298116\) \(6702564095567069184\) \([2, 2]\) \(7077888\) \(2.3394\)  
366912.et3 366912et1 \([0, 0, 0, -198156, 30419984]\) \(38272753/4368\) \(98206067334316032\) \([2]\) \(3538944\) \(1.9928\) \(\Gamma_0(N)\)-optimal
366912.et4 366912et3 \([0, 0, 0, 1213044, -1192130800]\) \(8780064047/32388174\) \(-728185713525536587776\) \([2]\) \(14155776\) \(2.6860\)  

Rank

sage: E.rank()
 

The elliptic curves in class 366912.et have rank \(0\).

Complex multiplication

The elliptic curves in class 366912.et do not have complex multiplication.

Modular form 366912.2.a.et

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 4 q^{11} - q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.