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Properties

Label 381150fo
Number of curves $2$
Conductor $381150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fo1")
 
E.isogeny_class()
 

Elliptic curves in class 381150fo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.fo2 381150fo1 \([1, -1, 0, -36867, 1179041]\) \(59319/28\) \(2615820539062500\) \([2]\) \(2073600\) \(1.6525\) \(\Gamma_0(N)\)-optimal
381150.fo1 381150fo2 \([1, -1, 0, -490617, 132312791]\) \(139798359/98\) \(9155371886718750\) \([2]\) \(4147200\) \(1.9991\)  

Rank

sage: E.rank()
 

The elliptic curves in class 381150fo have rank \(0\).

Complex multiplication

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

Modular form 381150.2.a.fo

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 2 q^{13} - q^{14} + q^{16} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.