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Properties

Label 374790.u
Number of curves $2$
Conductor $374790$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 374790.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374790.u1 374790u2 \([1, 1, 0, -2529852, -743911344]\) \(2017619016383881/898992282240\) \(797858959678590925440\) \([2]\) \(17203200\) \(2.7062\)  
374790.u2 374790u1 \([1, 1, 0, 545348, -86433584]\) \(20210333452919/15351398400\) \(-13624422588497510400\) \([2]\) \(8601600\) \(2.3597\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 374790.u have rank \(1\).

Complex multiplication

The elliptic curves in class 374790.u do not have complex multiplication.

Modular form 374790.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 2 q^{7} - q^{8} + q^{9} - q^{10} - 4 q^{11} - q^{12} - q^{13} + 2 q^{14} - q^{15} + q^{16} - q^{18} - 2 q^{19} + O(q^{20})\) 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.