Properties

Label 274890.n
Number of curves $8$
Conductor $274890$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 274890.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.n1 274890n7 \([1, 1, 0, -9860587643, 376875213421533]\) \(901247067798311192691198986281/552431869440\) \(64993057007746560\) \([2]\) \(191102976\) \(3.9337\)  
274890.n2 274890n8 \([1, 1, 0, -620426363, 5805359562717]\) \(224494757451893010998773801/6152490825146276160000\) \(723834393087634243947840000\) \([2]\) \(191102976\) \(3.9337\)  
274890.n3 274890n6 \([1, 1, 0, -616286843, 5888480296413]\) \(220031146443748723000125481/172266701724057600\) \(20267005191133652582400\) \([2, 2]\) \(95551488\) \(3.5872\)  
274890.n4 274890n4 \([1, 1, 0, -121760468, 516709162488]\) \(1696892787277117093383481/1440538624914939000\) \(169477928682617658411000\) \([2]\) \(63700992\) \(3.3844\)  
274890.n5 274890n5 \([1, 1, 0, -79741988, -271185960408]\) \(476646772170172569823801/5862293314453125000\) \(689692946152095703125000\) \([2]\) \(63700992\) \(3.3844\)  
274890.n6 274890n3 \([1, 1, 0, -38259323, 93291986397]\) \(-52643812360427830814761/1504091705903677440\) \(-176954885107861747138560\) \([2]\) \(47775744\) \(3.2406\)  
274890.n7 274890n2 \([1, 1, 0, -9305468, 4206745488]\) \(757443433548897303481/373234243041000000\) \(43910635459530609000000\) \([2, 2]\) \(31850496\) \(3.0379\)  
274890.n8 274890n1 \([1, 1, 0, 2125252, 505478352]\) \(9023321954633914439/6156756739584000\) \(-724336273655318016000\) \([2]\) \(15925248\) \(2.6913\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 274890.n have rank \(2\).

Complex multiplication

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

Modular form 274890.2.a.n

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 3 & 12 & 4 & 6 & 12 \\ 4 & 1 & 2 & 12 & 3 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 3 & 12 & 6 & 1 & 4 & 12 & 2 & 4 \\ 12 & 3 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.