Properties

Label 290145y
Number of curves $4$
Conductor $290145$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 290145y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
290145.y4 290145y1 \([1, 0, 1, -4415268, -3475856867]\) \(16003198512756001/488525390625\) \(290586295244384765625\) \([2]\) \(10321920\) \(2.7025\) \(\Gamma_0(N)\)-optimal
290145.y2 290145y2 \([1, 0, 1, -70118393, -225999200617]\) \(64096096056024006001/62562515625\) \(37213643314176890625\) \([2, 2]\) \(20643840\) \(3.0491\)  
290145.y3 290145y3 \([1, 0, 1, -69592768, -229554107617]\) \(-62665433378363916001/2004003001000125\) \(-1192027720348860673915125\) \([2]\) \(41287680\) \(3.3956\)  
290145.y1 290145y4 \([1, 0, 1, -1121894018, -14463675481117]\) \(262537424941059264096001/250125\) \(148780183165125\) \([2]\) \(41287680\) \(3.3956\)  

Rank

sage: E.rank()
 

The elliptic curves in class 290145y have rank \(1\).

Complex multiplication

The elliptic curves in class 290145y do not have complex multiplication.

Modular form 290145.2.a.y

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