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Properties

Label 90354p
Number of curves $2$
Conductor $90354$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 90354p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90354.q1 90354p1 \([1, 1, 1, -652357, -201137401]\) \(11966561852617/131736132\) \(337998872891909988\) \([2]\) \(1838592\) \(2.1781\) \(\Gamma_0(N)\)-optimal
90354.q2 90354p2 \([1, 1, 1, -145827, -504852789]\) \(-133667977897/42826704426\) \(-109881606556225386234\) \([2]\) \(3677184\) \(2.5247\)  

Rank

sage: E.rank()
 

The elliptic curves in class 90354p have rank \(1\).

Complex multiplication

The elliptic curves in class 90354p do not have complex multiplication.

Modular form 90354.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} + q^{9} + 2 q^{10} + q^{11} - q^{12} + 6 q^{13} + 2 q^{14} - 2 q^{15} + q^{16} + 2 q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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.