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Properties

Label 185150.c
Number of curves $2$
Conductor $185150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 185150.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185150.c1 185150bx2 \([1, 1, 0, -1312195, -579103465]\) \(-35716427480168065/98\) \(-685610450\) \([]\) \(1524096\) \(1.8145\)  
185150.c2 185150bx1 \([1, 1, 0, -16145, -805955]\) \(-66531687265/941192\) \(-6584602761800\) \([]\) \(508032\) \(1.2651\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 185150.c have rank \(0\).

Complex multiplication

The elliptic curves in class 185150.c do not have complex multiplication.

Modular form 185150.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} - 2 q^{9} - 3 q^{11} - q^{12} + 4 q^{13} + q^{14} + q^{16} - 6 q^{17} + 2 q^{18} + 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.