Properties

Label 397800.o
Number of curves $2$
Conductor $397800$
CM no
Rank $0$
Graph

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

Elliptic curves in class 397800.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
397800.o1 397800o1 \([0, 0, 0, -24075, 357750]\) \(132304644/71825\) \(837766800000000\) \([2]\) \(1572864\) \(1.5544\) \(\Gamma_0(N)\)-optimal
397800.o2 397800o2 \([0, 0, 0, 92925, 2814750]\) \(3804029838/2348125\) \(-54777060000000000\) \([2]\) \(3145728\) \(1.9010\)  

Rank

sage: E.rank()
 

The elliptic curves in class 397800.o have rank \(0\).

Complex multiplication

The elliptic curves in class 397800.o do not have complex multiplication.

Modular form 397800.2.a.o

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} + 2 q^{11} - q^{13} - q^{17} - 4 q^{19} + O(q^{20})\) 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.