↑

Properties

Label 479370.l
Number of curves $4$
Conductor $479370$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 479370.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
479370.l1 479370l4 \([1, 1, 0, -44424517262, -3603996993578664]\) \(16300610738133468173382620881/2228489100\) \(1325557287274301100\) \([2]\) \(604800000\) \(4.2925\)  
479370.l2 479370l3 \([1, 1, 0, -2776532082, -56313331184796]\) \(-3979640234041473454886161/1471455901872240\) \(-875256286256695914509040\) \([2]\) \(302400000\) \(3.9459\)  
479370.l3 479370l2 \([1, 1, 0, -73961762, -210962650764]\) \(75224183150104868881/11219310000000000\) \(6673507233528510000000000\) \([2]\) \(120960000\) \(3.4878\) \(\Gamma_0(N)\)-optimal*
479370.l4 479370l1 \([1, 1, 0, 7850718, -17999735436]\) \(89962967236397039/287450726400000\) \(-170982395701110374400000\) \([2]\) \(60480000\) \(3.1412\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 479370.l1.

Rank

sage: E.rank()
 

The elliptic curves in class 479370.l have rank \(1\).

Complex multiplication

The elliptic curves in class 479370.l do not have complex multiplication.

Modular form 479370.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 2 q^{7} - q^{8} + q^{9} - q^{10} - 2 q^{11} - q^{12} + 4 q^{13} + 2 q^{14} - q^{15} + q^{16} + 2 q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.