Properties

Label 1950.bb
Number of curves $2$
Conductor $1950$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1950.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.bb1 1950y2 \([1, 0, 0, -227906263, -1324307174983]\) \(-134057911417971280740025/1872\) \(-18281250000\) \([]\) \(168000\) \(2.9487\)  
1950.bb2 1950y1 \([1, 0, 0, -355303, -89334583]\) \(-198417696411528597145/22989483914821632\) \(-574737097870540800\) \([5]\) \(33600\) \(2.1440\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1950.bb have rank \(0\).

Complex multiplication

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

Modular form 1950.2.a.bb

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.