Properties

Label 17787.o
Number of curves $4$
Conductor $17787$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 17787.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17787.o1 17787u3 \([1, 0, 0, -868722, 311273073]\) \(347873904937/395307\) \(82390825805842323\) \([2]\) \(207360\) \(2.1593\)  
17787.o2 17787u2 \([1, 0, 0, -68307, 2152800]\) \(169112377/88209\) \(18384729725270601\) \([2, 2]\) \(103680\) \(1.8127\)  
17787.o3 17787u1 \([1, 0, 0, -38662, -2904637]\) \(30664297/297\) \(61901446886433\) \([2]\) \(51840\) \(1.4661\) \(\Gamma_0(N)\)-optimal
17787.o4 17787u4 \([1, 0, 0, 257788, 16827075]\) \(9090072503/5845851\) \(-1218406179065660739\) \([2]\) \(207360\) \(2.1593\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17787.o have rank \(0\).

Complex multiplication

The elliptic curves in class 17787.o do not have complex multiplication.

Modular form 17787.2.a.o

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.