Properties

Label 185.c
Number of curves $2$
Conductor $185$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 185.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185.c1 185c1 \([1, 0, 1, -4, -3]\) \(4826809/185\) \(185\) \([2]\) \(6\) \(-0.79707\) \(\Gamma_0(N)\)-optimal
185.c2 185c2 \([1, 0, 1, 1, -9]\) \(357911/34225\) \(-34225\) \([2]\) \(12\) \(-0.45050\)  

Rank

sage: E.rank()
 

The elliptic curves in class 185.c have rank \(1\).

Complex multiplication

The elliptic curves in class 185.c do not have complex multiplication.

Modular form 185.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{7} - 3 q^{8} + q^{9} - q^{10} + 2 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} - q^{16} + 2 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.