Properties

Label 770.e
Number of curves $2$
Conductor $770$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 770.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
770.e1 770a2 \([1, 1, 0, -73, -273]\) \(43949604889/42350\) \(42350\) \([2]\) \(128\) \(-0.19101\)  
770.e2 770a1 \([1, 1, 0, -3, -7]\) \(-4826809/10780\) \(-10780\) \([2]\) \(64\) \(-0.53759\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 770.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.