Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1950bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.v2 1950bb1 \([1, 0, 0, -323, -63]\) \(29819839301/17252352\) \(2156544000\) \([2]\) \(1792\) \(0.48045\) \(\Gamma_0(N)\)-optimal
1950.v1 1950bb2 \([1, 0, 0, -3523, 79937]\) \(38686490446661/141927552\) \(17740944000\) \([2]\) \(3584\) \(0.82703\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1950.2.a.bb

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.