Properties

Label 381150bs
Number of curves $4$
Conductor $381150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 381150bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.bs4 381150bs1 \([1, -1, 0, -2641392, 6042948016]\) \(-100999381393/723148272\) \(-14592544220714055750000\) \([2]\) \(23592960\) \(2.9361\) \(\Gamma_0(N)\)-optimal
381150.bs3 381150bs2 \([1, -1, 0, -68525892, 217861615516]\) \(1763535241378513/4612311396\) \(93072694234182417562500\) \([2, 2]\) \(47185920\) \(3.2826\)  
381150.bs1 381150bs3 \([1, -1, 0, -1095725142, 13960760381266]\) \(7209828390823479793/49509306\) \(999057544787804906250\) \([2]\) \(94371840\) \(3.6292\)  
381150.bs2 381150bs4 \([1, -1, 0, -95478642, 30566955766]\) \(4770223741048753/2740574865798\) \(55302572747259228504093750\) \([2]\) \(94371840\) \(3.6292\)  

Rank

sage: E.rank()
 

The elliptic curves in class 381150bs have rank \(1\).

Complex multiplication

The elliptic curves in class 381150bs do not have complex multiplication.

Modular form 381150.2.a.bs

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 2 q^{13} + q^{14} + q^{16} + 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.