Properties

Label 1850.a
Number of curves $2$
Conductor $1850$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1850.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.a1 1850g1 \([1, 0, 1, -476, 9498]\) \(-19026212425/51868672\) \(-32417920000\) \([3]\) \(1800\) \(0.70419\) \(\Gamma_0(N)\)-optimal
1850.a2 1850g2 \([1, 0, 1, 4149, -216202]\) \(12642252501575/39728447488\) \(-24830279680000\) \([]\) \(5400\) \(1.2535\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1850.a have rank \(1\).

Complex multiplication

The elliptic curves in class 1850.a do not have complex multiplication.

Modular form 1850.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} - 4 q^{7} - q^{8} + q^{9} - 2 q^{12} + 2 q^{13} + 4 q^{14} + q^{16} - q^{18} + 5 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.