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Properties

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

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Show commands: SageMath
E = EllipticCurve("hv1")
 
E.isogeny_class()
 

Elliptic curves in class 379050.hv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.hv1 379050hv2 \([1, 1, 1, -126538, 18278231]\) \(-7620530425/526848\) \(-15491267695680000\) \([]\) \(4478976\) \(1.8575\)  
379050.hv2 379050hv1 \([1, 1, 1, 8837, 29681]\) \(2595575/1512\) \(-44458357545000\) \([]\) \(1492992\) \(1.3082\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 379050.2.a.hv

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.