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Properties

Label 370678.l
Number of curves $2$
Conductor $370678$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 370678.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
370678.l1 370678l2 \([1, -1, 1, -100614168, -696127075737]\) \(-112642201262565356135544557649/144172805110421099950396844\) \(-144172805110421099950396844\) \([]\) \(220354176\) \(3.7126\)  
370678.l2 370678l1 \([1, -1, 1, -4227108, 3558433863]\) \(-8353214767445697278209809/632894185526315761664\) \(-632894185526315761664\) \([7]\) \(31479168\) \(2.7396\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 370678.l have rank \(1\).

Complex multiplication

The elliptic curves in class 370678.l do not have complex multiplication.

Modular form 370678.2.a.l

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.