Properties

Label 1850.p
Number of curves $2$
Conductor $1850$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1850.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.p1 1850i1 \([1, 1, 1, -11888, 1187281]\) \(-19026212425/51868672\) \(-506530000000000\) \([]\) \(9000\) \(1.5089\) \(\Gamma_0(N)\)-optimal
1850.p2 1850i2 \([1, 1, 1, 103737, -27025219]\) \(12642252501575/39728447488\) \(-387973120000000000\) \([]\) \(27000\) \(2.0582\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1850.p have rank \(0\).

Complex multiplication

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

Modular form 1850.2.a.p

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.