Properties

Label 101430.dn
Number of curves $4$
Conductor $101430$
CM no
Rank $0$
Graph

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

Elliptic curves in class 101430.dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.dn1 101430dr4 \([1, -1, 1, -1329464408, 51516688731]\) \(3029968325354577848895529/1753440696000000000000\) \(150385806899460216000000000000\) \([2]\) \(106168320\) \(4.2880\)  
101430.dn2 101430dr2 \([1, -1, 1, -914564993, 10645765390257]\) \(986396822567235411402169/6336721794060000\) \(543476048132687041260000\) \([2]\) \(35389440\) \(3.7387\)  
101430.dn3 101430dr1 \([1, -1, 1, -56061473, 173052650481]\) \(-227196402372228188089/19338934824115200\) \(-1658625424136177961139200\) \([2]\) \(17694720\) \(3.3922\) \(\Gamma_0(N)\)-optimal
101430.dn4 101430dr3 \([1, -1, 1, 332364712, 6314936667]\) \(47342661265381757089751/27397579603968000000\) \(-2349784127421051568128000000\) \([2]\) \(53084160\) \(3.9415\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101430.dn have rank \(0\).

Complex multiplication

The elliptic curves in class 101430.dn do not have complex multiplication.

Modular form 101430.2.a.dn

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 4q^{13} + q^{16} - 2q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

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

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

The vertices are labelled with LMFDB labels.