Properties

Label 379050.i
Number of curves $2$
Conductor $379050$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 379050.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.i1 379050i2 \([1, 1, 0, -51004277775, -4433636652694875]\) \(55296123367985268658129/148176000\) \(39321194330675250000000\) \([]\) \(744629760\) \(4.4561\)  
379050.i2 379050i1 \([1, 1, 0, -631781775, -6039445606875]\) \(105093573726037969/1444738498560\) \(383387615125835120640000000\) \([]\) \(248209920\) \(3.9068\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 379050.i have rank \(1\).

Complex multiplication

The elliptic curves in class 379050.i do not have complex multiplication.

Modular form 379050.2.a.i

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.