Properties

Label 770.g
Number of curves $4$
Conductor $770$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 770.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
770.g1 770g4 \([1, 0, 0, -3520, -80238]\) \(4823468134087681/30382271150\) \(30382271150\) \([2]\) \(1152\) \(0.84882\)  
770.g2 770g2 \([1, 0, 0, -270, 1612]\) \(2177286259681/105875000\) \(105875000\) \([6]\) \(384\) \(0.29951\)  
770.g3 770g3 \([1, 0, 0, -90, -2720]\) \(-80677568161/3131816380\) \(-3131816380\) \([2]\) \(576\) \(0.50224\)  
770.g4 770g1 \([1, 0, 0, 10, 100]\) \(109902239/4312000\) \(-4312000\) \([6]\) \(192\) \(-0.047062\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 770.g have rank \(0\).

Complex multiplication

The elliptic curves in class 770.g do not have complex multiplication.

Modular form 770.2.a.g

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

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.