Properties

Label 950a
Number of curves $2$
Conductor $950$
CM no
Rank $1$
Graph

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

Elliptic curves in class 950a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
950.b2 950a1 \([1, 0, 1, -1, 148]\) \(-1/608\) \(-9500000\) \([]\) \(160\) \(0.017785\) \(\Gamma_0(N)\)-optimal
950.b1 950a2 \([1, 0, 1, -1751, -31352]\) \(-37966934881/4952198\) \(-77378093750\) \([]\) \(800\) \(0.82250\)  

Rank

sage: E.rank()
 

The elliptic curves in class 950a have rank \(1\).

Complex multiplication

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

Modular form 950.2.a.a

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.