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Properties

Label 274890.cn
Number of curves $2$
Conductor $274890$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cn1")
 
E.isogeny_class()
 

Elliptic curves in class 274890.cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.cn1 274890cn2 \([1, 0, 1, -35236318, 80200431056]\) \(41125104693338423360329/179205840000000000\) \(21083387870160000000000\) \([2]\) \(35942400\) \(3.1366\)  
274890.cn2 274890cn1 \([1, 0, 1, -1116638, 2489447888]\) \(-1308796492121439049/22000592486400000\) \(-2588347705432473600000\) \([2]\) \(17971200\) \(2.7900\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 274890.cn have rank \(0\).

Complex multiplication

The elliptic curves in class 274890.cn do not have complex multiplication.

Modular form 274890.2.a.cn

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.