↑

Properties

Label 122094.be
Number of curves $3$
Conductor $122094$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 122094.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122094.be1 122094bl2 \([1, -1, 1, -426456524, -3389585226281]\) \(435769376173654361409706491/45550077714003688\) \(896562179644734590904\) \([]\) \(31492800\) \(3.4493\)  
122094.be2 122094bl3 \([1, -1, 1, -193010459, 1031970436427]\) \(3272351648557113352874597691/631541606162039308288\) \(153464610297375551913984\) \([9]\) \(31492800\) \(3.4493\)  
122094.be3 122094bl1 \([1, -1, 1, -5862644, -3527169193]\) \(825354356328003992536899/278415399987999672832\) \(7517215799675991166464\) \([3]\) \(10497600\) \(2.9000\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 122094.be have rank \(0\).

Complex multiplication

The elliptic curves in class 122094.be do not have complex multiplication.

Modular form 122094.2.a.be

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

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.