Properties

Label 1950.i
Number of curves $2$
Conductor $1950$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1950.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.i1 1950j2 \([1, 0, 1, -66, 178]\) \(248858189/27378\) \(3422250\) \([2]\) \(512\) \(-0.012751\)  
1950.i2 1950j1 \([1, 0, 1, -16, -22]\) \(3307949/468\) \(58500\) \([2]\) \(256\) \(-0.35932\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1950.i have rank \(1\).

Complex multiplication

The elliptic curves in class 1950.i do not have complex multiplication.

Modular form 1950.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.