Properties

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

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

Elliptic curves in class 1950.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.a1 1950b1 \([1, 1, 0, -9116250, -10598103900]\) \(-134057911417971280740025/1872\) \(-1170000\) \([]\) \(33600\) \(2.1440\) \(\Gamma_0(N)\)-optimal
1950.a2 1950b2 \([1, 1, 0, -8882575, -11166822875]\) \(-198417696411528597145/22989483914821632\) \(-8980267154227200000000\) \([]\) \(168000\) \(2.9487\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1950.2.a.a

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.