Properties

Label 714.i
Number of curves $3$
Conductor $714$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 714.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
714.i1 714i3 \([1, 0, 0, -381702, -90803346]\) \(-6150311179917589675873/244053849830826\) \(-244053849830826\) \([]\) \(9720\) \(1.8441\)  
714.i2 714i2 \([1, 0, 0, -972, -315144]\) \(-101566487155393/42823570577256\) \(-42823570577256\) \([3]\) \(3240\) \(1.2948\)  
714.i3 714i1 \([1, 0, 0, 108, 11664]\) \(139233463487/58763045376\) \(-58763045376\) \([9]\) \(1080\) \(0.74550\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 714.i have rank \(0\).

Complex multiplication

The elliptic curves in class 714.i do not have complex multiplication.

Modular form 714.2.a.i

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.