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Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 1850.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.e1 1850f2 \([1, -1, 0, -13657, -610899]\) \(2253707317528029/700928\) \(87616000\) \([2]\) \(1728\) \(0.88632\)  
1850.e2 1850f1 \([1, -1, 0, -857, -9299]\) \(557238592989/9699328\) \(1212416000\) \([2]\) \(864\) \(0.53975\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1850.2.a.e

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