↑

Properties

Label 17787.m
Number of curves $2$
Conductor $17787$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 17787.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17787.m1 17787s2 \([1, 0, 0, -21110328, 23058853929]\) \(14553591673375/5208653241\) \(372360767602793775428007\) \([2]\) \(2150400\) \(3.2237\)  
17787.m2 17787s1 \([1, 0, 0, 3998987, 2534499848]\) \(98931640625/96059601\) \(-6867192940091151779727\) \([2]\) \(1075200\) \(2.8771\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 17787.2.a.m

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