Properties

Label 468270.l
Number of curves $2$
Conductor $468270$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 468270.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
468270.l1 468270l2 \([1, -1, 0, -21196500210, 1187808122415316]\) \(815516123997553004685843001/168699801600\) \(217870390143054950400\) \([2]\) \(389283840\) \(4.1998\) \(\Gamma_0(N)\)-optimal*
468270.l2 468270l1 \([1, -1, 0, -1324776690, 18559884843220]\) \(-199098554419711270541881/2863609298288640\) \(-3698259684470345076572160\) \([2]\) \(194641920\) \(3.8532\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 468270.l1.

Rank

sage: E.rank()
 

The elliptic curves in class 468270.l have rank \(1\).

Complex multiplication

The elliptic curves in class 468270.l do not have complex multiplication.

Modular form 468270.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + q^{16} + 8 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.