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Properties

Label 34650.dn
Number of curves $4$
Conductor $34650$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dn1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 34650.dn have rank \(0\).

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 \(\mathbb{F}_p\)
\(13\) \( 1 - 4 T + 13 T^{2}\) 1.13.ae
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(19\) \( 1 - 8 T + 19 T^{2}\) 1.19.ai
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 34650.2.a.dn

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 34650.dn

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34650.dn1 34650dd3 \([1, -1, 1, -5458730, 4910279397]\) \(1579250141304807889/41926500\) \(477569039062500\) \([2]\) \(995328\) \(2.3307\)  
34650.dn2 34650dd4 \([1, -1, 1, -5451980, 4923023397]\) \(-1573398910560073969/8138108343750\) \(-92698140353027343750\) \([2]\) \(1990656\) \(2.6773\)  
34650.dn3 34650dd1 \([1, -1, 1, -72230, 5729397]\) \(3658671062929/880165440\) \(10025634465000000\) \([2]\) \(331776\) \(1.7814\) \(\Gamma_0(N)\)-optimal
34650.dn4 34650dd2 \([1, -1, 1, 170770, 35861397]\) \(48351870250991/76871856600\) \(-875618491584375000\) \([2]\) \(663552\) \(2.1280\)