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Properties

Label 417450p
Number of curves $2$
Conductor $417450$
CM no
Rank $0$
Graph

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

Elliptic curves in class 417450p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
417450.p1 417450p1 \([1, 1, 0, -540025, 26873125]\) \(472729139/264960\) \(9761903440740000000\) \([2]\) \(11354112\) \(2.3339\) \(\Gamma_0(N)\)-optimal
417450.p2 417450p2 \([1, 1, 0, 2121975, 215875125]\) \(28680715981/17139600\) \(-631473128822868750000\) \([2]\) \(22708224\) \(2.6805\)  

Rank

sage: E.rank()
 

The elliptic curves in class 417450p have rank \(0\).

Complex multiplication

The elliptic curves in class 417450p do not have complex multiplication.

Modular form 417450.2.a.p

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