Properties

Label 274890c
Number of curves $4$
Conductor $274890$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 274890c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.c3 274890c1 \([1, 1, 0, -3178263, 2103559893]\) \(30179023393892020201/1196047835136000\) \(140713831755915264000\) \([2]\) \(11796480\) \(2.6328\) \(\Gamma_0(N)\)-optimal
274890.c2 274890c2 \([1, 1, 0, -8258583, -6308433963]\) \(529483179157097938921/160443506916000000\) \(18876018145160484000000\) \([2, 2]\) \(23592960\) \(2.9794\)  
274890.c4 274890c3 \([1, 1, 0, 22611417, -42321375963]\) \(10867228028544202381079/12868640151403806000\) \(-1513982645172506372094000\) \([2]\) \(47185920\) \(3.3260\)  
274890.c1 274890c4 \([1, 1, 0, -120413703, -508561492347]\) \(1641206446466677841336041/268339886718750000\) \(31569919332574218750000\) \([2]\) \(47185920\) \(3.3260\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 274890.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.