Properties

Label 350.e
Number of curves $2$
Conductor $350$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 350.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350.e1 350b2 \([1, 0, 0, -1138, -20858]\) \(-417267265/235298\) \(-91913281250\) \([]\) \(360\) \(0.80685\)  
350.e2 350b1 \([1, 0, 0, 112, 392]\) \(397535/392\) \(-153125000\) \([3]\) \(120\) \(0.25755\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 350.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.