Properties

Label 1900.a
Number of curves $2$
Conductor $1900$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1900.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1900.a1 1900a1 \([0, 1, 0, -23033, 1247188]\) \(5405726654464/407253125\) \(101813281250000\) \([2]\) \(5760\) \(1.4331\) \(\Gamma_0(N)\)-optimal
1900.a2 1900a2 \([0, 1, 0, 22092, 5579188]\) \(298091207216/3525390625\) \(-14101562500000000\) \([2]\) \(11520\) \(1.7797\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1900.a have rank \(0\).

Complex multiplication

The elliptic curves in class 1900.a do not have complex multiplication.

Modular form 1900.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - 2q^{7} + q^{9} - 6q^{13} - 2q^{17} - q^{19} + O(q^{20})\)  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 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.