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Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 279174.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
279174.q1 279174q1 \([1, 1, 0, -322674, 16635060]\) \(153930331718857/84047007744\) \(2028690448664334336\) \([2]\) \(5971968\) \(2.2036\) \(\Gamma_0(N)\)-optimal
279174.q2 279174q2 \([1, 1, 0, 1249486, 132660468]\) \(8937659885072183/5484762497088\) \(-132388833222073899072\) \([2]\) \(11943936\) \(2.5502\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 279174.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - 2 q^{10} + 4 q^{11} - q^{12} + 2 q^{13} - q^{14} - 2 q^{15} + q^{16} - q^{18} + O(q^{20})\) 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 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.