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Properties

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

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Show commands: SageMath
E = EllipticCurve("gr1")
 
E.isogeny_class()
 

Elliptic curves in class 381150.gr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.gr1 381150gr2 \([1, -1, 0, -4610667, -3435650509]\) \(10896752313/1176490\) \(1170324230196623906250\) \([2]\) \(17031168\) \(2.7766\)  
381150.gr2 381150gr1 \([1, -1, 0, 380583, -266206759]\) \(6128487/34300\) \(-34120239947423437500\) \([2]\) \(8515584\) \(2.4301\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 381150.2.a.gr

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