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Properties

Label 351726w
Number of curves $2$
Conductor $351726$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 351726w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
351726.w2 351726w1 \([1, 1, 1, -4825, -997561]\) \(-13997521/474336\) \(-420974946030816\) \([]\) \(1728000\) \(1.4864\) \(\Gamma_0(N)\)-optimal
351726.w1 351726w2 \([1, 1, 1, -494935, 168234539]\) \(-15107691357361/5067577806\) \(-4497493956578903886\) \([]\) \(8640000\) \(2.2912\)  

Rank

sage: E.rank()
 

The elliptic curves in class 351726w have rank \(1\).

Complex multiplication

The elliptic curves in class 351726w do not have complex multiplication.

Modular form 351726.2.a.w

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.