Properties

Label 350727f
Number of curves $2$
Conductor $350727$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 350727f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350727.f2 350727f1 \([1, 0, 0, -17468, 841095]\) \(3981876625/232713\) \(34449875836857\) \([2]\) \(720896\) \(1.3511\) \(\Gamma_0(N)\)-optimal
350727.f1 350727f2 \([1, 0, 0, -51853, -3498292]\) \(104154702625/24649677\) \(3649036848257853\) \([2]\) \(1441792\) \(1.6976\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350727f have rank \(1\).

Complex multiplication

The elliptic curves in class 350727f do not have complex multiplication.

Modular form 350727.2.a.f

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