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Properties

Label 950.a
Number of curves $2$
Conductor $950$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 950.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
950.a1 950b2 \([1, 1, 0, -69500, -7081250]\) \(-2376117230685121/342950\) \(-5358593750\) \([]\) \(1728\) \(1.2759\)  
950.a2 950b1 \([1, 1, 0, -750, -12500]\) \(-2992209121/2375000\) \(-37109375000\) \([]\) \(576\) \(0.72655\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 950.a have rank \(0\).

Complex multiplication

The elliptic curves in class 950.a do not have complex multiplication.

Modular form 950.2.a.a

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