Properties

Label 370.d
Number of curves $4$
Conductor $370$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 370.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
370.d1 370d3 \([1, 0, 0, -5275, -147903]\) \(16232905099479601/4052240\) \(4052240\) \([2]\) \(288\) \(0.64351\)  
370.d2 370d4 \([1, 0, 0, -5255, -149075]\) \(-16048965315233521/256572640900\) \(-256572640900\) \([2]\) \(576\) \(0.99008\)  
370.d3 370d1 \([1, 0, 0, -75, -143]\) \(46694890801/18944000\) \(18944000\) \([6]\) \(96\) \(0.094202\) \(\Gamma_0(N)\)-optimal
370.d4 370d2 \([1, 0, 0, 245, -975]\) \(1625964918479/1369000000\) \(-1369000000\) \([6]\) \(192\) \(0.44078\)  

Rank

sage: E.rank()
 

The elliptic curves in class 370.d have rank \(0\).

Complex multiplication

The elliptic curves in class 370.d do not have complex multiplication.

Modular form 370.2.a.d

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.