Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 374790df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374790.df2 374790df1 \([1, 0, 0, 3824, 252956]\) \(6967871/35100\) \(-31151379203100\) \([2]\) \(1474560\) \(1.2714\) \(\Gamma_0(N)\)-optimal
374790.df1 374790df2 \([1, 0, 0, -44226, 3203226]\) \(10779215329/1232010\) \(1093413410028810\) \([2]\) \(2949120\) \(1.6180\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 374790.2.a.df

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} + q^{13} + 2q^{14} - q^{15} + q^{16} - 8q^{17} + q^{18} - 6q^{19} + O(q^{20})\)  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.