Properties

Label 350.b
Number of curves $4$
Conductor $350$
CM no
Rank $0$
Graph

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

Elliptic curves in class 350.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350.b1 350a3 \([1, -1, 0, -6692, -209034]\) \(2121328796049/120050\) \(1875781250\) \([2]\) \(384\) \(0.84371\)  
350.b2 350a4 \([1, -1, 0, -2192, 37466]\) \(74565301329/5468750\) \(85449218750\) \([2]\) \(384\) \(0.84371\)  
350.b3 350a2 \([1, -1, 0, -442, -2784]\) \(611960049/122500\) \(1914062500\) \([2, 2]\) \(192\) \(0.49713\)  
350.b4 350a1 \([1, -1, 0, 58, -284]\) \(1367631/2800\) \(-43750000\) \([2]\) \(96\) \(0.15056\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 350.b have rank \(0\).

Complex multiplication

The elliptic curves in class 350.b do not have complex multiplication.

Modular form 350.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.