Properties

Label 370.b
Number of curves $4$
Conductor $370$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 370.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
370.b1 370a3 \([1, -1, 0, -395, -2925]\) \(6825481747209/46250\) \(46250\) \([2]\) \(64\) \(0.076511\)  
370.b2 370a2 \([1, -1, 0, -25, -39]\) \(1767172329/136900\) \(136900\) \([2, 2]\) \(32\) \(-0.27006\)  
370.b3 370a1 \([1, -1, 0, -5, 5]\) \(15438249/2960\) \(2960\) \([2]\) \(16\) \(-0.61664\) \(\Gamma_0(N)\)-optimal
370.b4 370a4 \([1, -1, 0, 25, -209]\) \(1689410871/18741610\) \(-18741610\) \([2]\) \(64\) \(0.076511\)  

Rank

sage: E.rank()
 

The elliptic curves in class 370.b have rank \(1\).

Complex multiplication

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

Modular form 370.2.a.b

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.