Properties

Label 770.b
Number of curves $2$
Conductor $770$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 770.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
770.b1 770d2 \([1, 0, 1, -848, 9006]\) \(67324767141241/3368750000\) \(3368750000\) \([2]\) \(512\) \(0.58688\)  
770.b2 770d1 \([1, 0, 1, 32, 558]\) \(3789119879/135520000\) \(-135520000\) \([2]\) \(256\) \(0.24031\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 770.b have rank \(1\).

Complex multiplication

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

Modular form 770.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.