Properties

Label 714.d
Number of curves $2$
Conductor $714$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("714.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 714.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
714.d1 714a2 [1, 1, 0, -55174, 4965268] [2] 2688  
714.d2 714a1 [1, 1, 0, -3334, 81940] [2] 1344 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 714.d have rank \(1\).

Modular form 714.2.a.d

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.