Properties

Label 171.c
Number of curves $2$
Conductor $171$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 171.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
171.c1 171c2 \([0, 0, 1, -39513, 3023145]\) \(-9358714467168256/22284891\) \(-16245685539\) \([]\) \(480\) \(1.2007\)  
171.c2 171c1 \([0, 0, 1, 177, 1035]\) \(841232384/1121931\) \(-817887699\) \([]\) \(96\) \(0.39599\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 171.c have rank \(0\).

Complex multiplication

The elliptic curves in class 171.c do not have complex multiplication.

Modular form 171.2.a.c

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.