Properties

Label 327990.o
Number of curves $2$
Conductor $327990$
CM no
Rank $0$
Graph

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

Elliptic curves in class 327990.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.o1 327990o1 \([1, 0, 1, -63934, 7009232]\) \(-40861808665609/6406452000\) \(-4531161777012000\) \([3]\) \(2268000\) \(1.7327\) \(\Gamma_0(N)\)-optimal
327990.o2 327990o2 \([1, 0, 1, 428051, -25264984]\) \(12263649421047431/7488000000000\) \(-5296120128000000000\) \([]\) \(6804000\) \(2.2820\)  

Rank

sage: E.rank()
 

The elliptic curves in class 327990.o have rank \(0\).

Complex multiplication

The elliptic curves in class 327990.o do not have complex multiplication.

Modular form 327990.2.a.o

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.