Properties

Label 189.c
Number of curves $3$
Conductor $189$
CM no
Rank $0$
Graph

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

Elliptic curves in class 189.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189.c1 189c3 \([0, 0, 1, -426, 3384]\) \(35184082944/7\) \(1701\) \([3]\) \(36\) \(0.0093281\)  
189.c2 189c2 \([0, 0, 1, -216, -1222]\) \(56623104/7\) \(137781\) \([]\) \(36\) \(0.0093281\)  
189.c3 189c1 \([0, 0, 1, -6, 3]\) \(884736/343\) \(9261\) \([3]\) \(12\) \(-0.53998\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 189.c have rank \(0\).

Complex multiplication

The elliptic curves in class 189.c do not have complex multiplication.

Modular form 189.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.