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Properties

Label 122034a
Number of curves $2$
Conductor $122034$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 122034a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122034.a1 122034a1 \([1, 1, 0, -144260, 19458768]\) \(52523718625/4359168\) \(27555883519583232\) \([2]\) \(1182720\) \(1.8967\) \(\Gamma_0(N)\)-optimal
122034.a2 122034a2 \([1, 1, 0, 151580, 89336176]\) \(60930425375/579905568\) \(-3665793629464556832\) \([2]\) \(2365440\) \(2.2433\)  

Rank

sage: E.rank()
 

The elliptic curves in class 122034a have rank \(0\).

Complex multiplication

The elliptic curves in class 122034a do not have complex multiplication.

Modular form 122034.2.a.a

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