Properties

Label 331298.o
Number of curves $2$
Conductor $331298$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 331298.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
331298.o1 331298o2 \([1, 0, 0, -8617199, -10001302343]\) \(-128667913/4096\) \(-2252743647172150595584\) \([]\) \(26516160\) \(2.8732\)  
331298.o2 331298o1 \([1, 0, 0, 493496, -50601264]\) \(24167/16\) \(-8799779871766213264\) \([]\) \(8838720\) \(2.3239\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 331298.o have rank \(1\).

Complex multiplication

The elliptic curves in class 331298.o do not have complex multiplication.

Modular form 331298.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} + q^{8} + q^{9} + 3 q^{10} - 2 q^{12} - 5 q^{13} + 2 q^{14} - 6 q^{15} + q^{16} - 3 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.