Properties

Label 700.d
Number of curves $2$
Conductor $700$
CM no
Rank $0$
Graph

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

Elliptic curves in class 700.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
700.d1 700a2 \([0, -1, 0, -20133, -1092863]\) \(-225637236736/1715\) \(-6860000000\) \([]\) \(864\) \(1.0623\)  
700.d2 700a1 \([0, -1, 0, -133, -2863]\) \(-65536/875\) \(-3500000000\) \([]\) \(288\) \(0.51296\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 700.d have rank \(0\).

Complex multiplication

The elliptic curves in class 700.d do not have complex multiplication.

Modular form 700.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} - 2q^{9} + 3q^{11} + q^{13} + 3q^{17} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.