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Properties

Label 92480.dn
Number of curves $4$
Conductor $92480$
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 92480.dn have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(5\)\(1 + T\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 - 2 T + 3 T^{2}\) 1.3.ac
\(7\) \( 1 - 2 T + 7 T^{2}\) 1.7.ac
\(11\) \( 1 + 6 T + 11 T^{2}\) 1.11.g
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(19\) \( 1 - 8 T + 19 T^{2}\) 1.19.ai
\(23\) \( 1 + 6 T + 23 T^{2}\) 1.23.g
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 92480.dn do not have complex multiplication.

Modular form 92480.2.a.dn

Copy content sage:E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{5} + 2 q^{7} + q^{9} - 6 q^{11} - 2 q^{13} - 2 q^{15} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 92480.dn

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92480.dn1 92480di3 \([0, -1, 0, -77100961, 51281572161]\) \(8010684753304969/4456448000000\) \(28198258893104611328000000\) \([2]\) \(26542080\) \(3.5738\)  
92480.dn2 92480di1 \([0, -1, 0, -47229921, -124914486655]\) \(1841373668746009/31443200\) \(198957441897149235200\) \([2]\) \(8847360\) \(3.0245\) \(\Gamma_0(N)\)-optimal
92480.dn3 92480di2 \([0, -1, 0, -45750241, -133108658559]\) \(-1673672305534489/241375690000\) \(-1527309237563584675840000\) \([2]\) \(17694720\) \(3.3711\)  
92480.dn4 92480di4 \([0, -1, 0, 301697119, 405760815425]\) \(479958568556831351/289000000000000\) \(-1828652958613504000000000000\) \([2]\) \(53084160\) \(3.9204\)