Properties

Label 88935.m
Number of curves $2$
Conductor $88935$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 88935.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.m1 88935g2 \([1, 1, 1, -201286, 25517834]\) \(1115157653/295245\) \(238787087248048185\) \([2]\) \(1013760\) \(2.0431\)  
88935.m2 88935g1 \([1, 1, 1, 31639, 2598014]\) \(4330747/6075\) \(-4913314552428975\) \([2]\) \(506880\) \(1.6965\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 88935.m have rank \(0\).

Complex multiplication

The elliptic curves in class 88935.m do not have complex multiplication.

Modular form 88935.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 3 q^{8} + q^{9} + q^{10} + q^{12} + 2 q^{13} + q^{15} - q^{16} - q^{18} - 4 q^{19} + O(q^{20})\) 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.