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Properties

Label 324870.fz
Number of curves $2$
Conductor $324870$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fz1")
 
E.isogeny_class()
 

Elliptic curves in class 324870.fz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
324870.fz1 324870fz2 \([1, 0, 0, -12357640, 16319057600]\) \(4259260985149239673931089/116663388120630000000\) \(5716506017910870000000\) \([7]\) \(31347456\) \(2.9547\)  
324870.fz2 324870fz1 \([1, 0, 0, -1583240, -766907478]\) \(8957110050243238628689/32001743670\) \(1568085439830\) \([]\) \(4478208\) \(1.9817\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 324870.fz have rank \(0\).

Complex multiplication

The elliptic curves in class 324870.fz do not have complex multiplication.

Modular form 324870.2.a.fz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} - q^{13} + q^{15} + q^{16} + q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.