Properties

Label 76050bo
Number of curves $2$
Conductor $76050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 76050bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76050.u1 76050bo1 \([1, -1, 0, -2358342, -2440148684]\) \(-156116857/186624\) \(-1734051000395844000000\) \([]\) \(4313088\) \(2.7692\) \(\Gamma_0(N)\)-optimal
76050.u2 76050bo2 \([1, -1, 0, 19886283, 45630485941]\) \(93603087383/150994944\) \(-1402997115579531264000000\) \([]\) \(12939264\) \(3.3185\)  

Rank

sage: E.rank()
 

The elliptic curves in class 76050bo have rank \(0\).

Complex multiplication

The elliptic curves in class 76050bo do not have complex multiplication.

Modular form 76050.2.a.bo

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{7} - q^{8} - 6 q^{11} + 2 q^{14} + q^{16} - 3 q^{17} + 2 q^{19} + O(q^{20})\) Copy content 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 Cremona 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 Cremona labels.