Properties

Label 370.a
Number of curves $3$
Conductor $370$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 370.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
370.a1 370c3 \([1, 0, 1, -54, 146]\) \(-16954786009/370\) \(-370\) \([3]\) \(324\) \(-0.39121\)  
370.a2 370c1 \([1, 0, 1, -19, 342]\) \(-702595369/50653000\) \(-50653000\) \([3]\) \(108\) \(0.15809\) \(\Gamma_0(N)\)-optimal
370.a3 370c2 \([1, 0, 1, 166, -9204]\) \(510273943271/37000000000\) \(-37000000000\) \([]\) \(324\) \(0.70740\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 370.2.a.a

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.