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Properties

Label 182070.ee
Number of curves $2$
Conductor $182070$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ee1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 182070.ee have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(5\)\(1 - T\)
\(7\)\(1 - T\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 6 T + 11 T^{2}\) 1.11.ag
\(13\) \( 1 + 4 T + 13 T^{2}\) 1.13.e
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 + 8 T + 29 T^{2}\) 1.29.i
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 182070.ee do not have complex multiplication.

Modular form 182070.2.a.ee

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + 6 q^{11} - 4 q^{13} + q^{14} + q^{16} + O(q^{20})\) 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 182070.ee

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.ee1 182070o2 \([1, -1, 1, -1069458962, 13461793218321]\) \(37769548376817211811066153/1011738331054080\) \(3623618736521678684160\) \([2]\) \(70778880\) \(3.6503\)  
182070.ee2 182070o1 \([1, -1, 1, -66758162, 210901606161]\) \(-9186763300983704416553/47730830553907200\) \(-170951644902771287654400\) \([2]\) \(35389440\) \(3.3038\) \(\Gamma_0(N)\)-optimal