Properties

Label 1850.o
Number of curves $3$
Conductor $1850$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1850.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.o1 1850h1 \([1, 1, 1, -1338, 18281]\) \(-16954786009/370\) \(-5781250\) \([]\) \(864\) \(0.41351\) \(\Gamma_0(N)\)-optimal
1850.o2 1850h2 \([1, 1, 1, -463, 42781]\) \(-702595369/50653000\) \(-791453125000\) \([]\) \(2592\) \(0.96281\)  
1850.o3 1850h3 \([1, 1, 1, 4162, -1150469]\) \(510273943271/37000000000\) \(-578125000000000\) \([]\) \(7776\) \(1.5121\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1850.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{7} + q^{8} + q^{9} + 3 q^{11} + 2 q^{12} + 4 q^{13} + q^{14} + q^{16} - 3 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.