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Properties

Label 34650.n
Number of curves $8$
Conductor $34650$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("n1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 34650.n have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1 + T\)
\(11\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 34650.n do not have complex multiplication.

Modular form 34650.2.a.n

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + q^{11} - 2 q^{13} + q^{14} + q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 6 & 12 & 12 & 4 \\ 2 & 1 & 6 & 2 & 3 & 6 & 6 & 2 \\ 3 & 6 & 1 & 12 & 2 & 4 & 4 & 12 \\ 4 & 2 & 12 & 1 & 6 & 3 & 12 & 4 \\ 6 & 3 & 2 & 6 & 1 & 2 & 2 & 6 \\ 12 & 6 & 4 & 3 & 2 & 1 & 4 & 12 \\ 12 & 6 & 4 & 12 & 2 & 4 & 1 & 3 \\ 4 & 2 & 12 & 4 & 6 & 12 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 34650.n

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34650.n1 34650s8 \([1, -1, 0, -5730297417, 166961376217741]\) \(1826870018430810435423307849/7641104625000000000\) \(87036957369140625000000000\) \([2]\) \(31850496\) \(4.1863\)  
34650.n2 34650s6 \([1, -1, 0, -363705417, 2523630745741]\) \(467116778179943012100169/28800309694464000000\) \(328053527613504000000000000\) \([2, 2]\) \(15925248\) \(3.8397\)  
34650.n3 34650s5 \([1, -1, 0, -98499042, 33064007116]\) \(9278380528613437145689/5328033205714065000\) \(60689628233836771640625000\) \([2]\) \(10616832\) \(3.6370\)  
34650.n4 34650s3 \([1, -1, 0, -68793417, -170980198259]\) \(3160944030998056790089/720291785342976000\) \(8204573617422336000000000\) \([2]\) \(7962624\) \(3.4931\)  
34650.n5 34650s2 \([1, -1, 0, -64542042, -198760431884]\) \(2610383204210122997209/12104550027662400\) \(137878390158842025000000\) \([2, 2]\) \(5308416\) \(3.2904\)  
34650.n6 34650s1 \([1, -1, 0, -64470042, -199227783884]\) \(2601656892010848045529/56330588160\) \(641640605760000000\) \([2]\) \(2654208\) \(2.9438\) \(\Gamma_0(N)\)-optimal
34650.n7 34650s4 \([1, -1, 0, -31737042, -400675206884]\) \(-310366976336070130009/5909282337130963560\) \(-67310419121382381800625000\) \([2]\) \(10616832\) \(3.6370\)  
34650.n8 34650s7 \([1, -1, 0, 284294583, 10537446745741]\) \(223090928422700449019831/4340371122724101696000\) \(-49439539819779220881000000000\) \([2]\) \(31850496\) \(4.1863\)