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Properties

Label 279174bg
Number of curves $2$
Conductor $279174$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 279174bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
279174.bg1 279174bg1 \([1, 0, 1, -12006656, -16014297346]\) \(1614171115147625/1877904\) \(222696647625222288\) \([2]\) \(10027008\) \(2.6121\) \(\Gamma_0(N)\)-optimal
279174.bg2 279174bg2 \([1, 0, 1, -11908396, -16289268130]\) \(-1574864421763625/55101928644\) \(-6534420708781178680068\) \([2]\) \(20054016\) \(2.9587\)  

Rank

sage: E.rank()
 

The elliptic curves in class 279174bg have rank \(0\).

Complex multiplication

The elliptic curves in class 279174bg do not have complex multiplication.

Modular form 279174.2.a.bg

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