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Properties

Label 327600.nt
Number of curves $2$
Conductor $327600$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("nt1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 327600.nt have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1 - T\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 6 T + 11 T^{2}\) 1.11.ag
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 6 T + 23 T^{2}\) 1.23.g
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 327600.nt do not have complex multiplication.

Modular form 327600.2.a.nt

Copy content sage:E.q_eigenform(10)
 
\(q + q^{7} + 6 q^{11} - q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 327600.nt

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327600.nt1 327600nt2 \([0, 0, 0, -1799355, -924512150]\) \(1726143065560493/9662982966\) \(3606689066093568000\) \([2]\) \(8110080\) \(2.4031\)  
327600.nt2 327600nt1 \([0, 0, 0, -49755, -30466550]\) \(-36495256013/1053197964\) \(-393104033667072000\) \([2]\) \(4055040\) \(2.0565\) \(\Gamma_0(N)\)-optimal