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Properties

Label 279174.bl
Number of curves $2$
Conductor $279174$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 279174.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
279174.bl1 279174bl2 \([1, 0, 1, -967145, 319727756]\) \(4144806984356137/568114785504\) \(13712909835022999776\) \([2]\) \(9953280\) \(2.3989\)  
279174.bl2 279174bl1 \([1, 0, 1, 96375, 26621644]\) \(4101378352343/15049939968\) \(-363268964423457792\) \([2]\) \(4976640\) \(2.0524\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 279174.2.a.bl

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - 2 q^{10} + q^{12} + 4 q^{13} - q^{14} + 2 q^{15} + q^{16} - q^{18} + 6 q^{19} + O(q^{20})\) 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.